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"target_action": "place both coordinate parentheses inside the math node and remove the stray prose parenthesis",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C019",
"native": {
"category": "mathematical_domain",
"evidence": "the table and every subsequent quantifier use X",
"file": "repo/source/sec_metric_space.ptx",
"id": "O003-C019",
"source_issue": "the finite example declares X={a,b,c} but gives d the unrelated domain A times A",
"source_locator": "authority line 126",
"status": "verified",
"target_action": "replace A times A with X times X",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C020",
"native": {
"category": "missing_case",
"evidence": "the proof now exhausts x=y x=z z=y and the three all-distinct inequalities",
"file": "repo/source/sec_metric_space.ptx",
"id": "O003-C020",
"source_issue": "the finite-metric proof quantifies only x and y although z occurs and then claims only the all-distinct cases remain without treating z=y",
"source_locator": "authority lines 168-175",
"status": "verified",
"target_action": "quantify x y z and add the z=y degenerate triangle case",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C021",
"native": {
"category": "mathematical_operator",
"evidence": "both expanded expressions now match the summation formula beside them",
"file": "repo/source/sec_euclid_rn.ptx",
"id": "O003-C021",
"source_issue": "both expanded Euclidean-distance formulas omit the plus sign before the final squared coordinate difference",
"source_locator": "authority lines 23 and 277",
"status": "verified",
"target_action": "insert the missing plus signs",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C022",
"native": {
"category": "missing_hypothesis",
"evidence": "the denominator 2a and discriminant argument now have their required hypothesis",
"file": "repo/source/sec_euclid_rn.ptx",
"id": "O003-C022",
"source_issue": "the Cauchy-Schwarz proof treats a=sum y_i^2 as a positive quadratic coefficient without handling y=0",
"source_locator": "authority lines 149-150",
"status": "verified",
"target_action": "dispose of y=0 separately and state y nonzero hence a>0 before using the quadratic formula",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C023",
"native": {
"category": "mathematical_delimiter",
"evidence": "the formula now matches the chapter introduction and summary definitions of d_T",
"file": "repo/source/sec_euclid_rn.ptx",
"id": "O003-C023",
"source_issue": "the closing taxicab formula encloses each absolute coordinate difference in literal set braces",
"source_locator": "authority line 286",
"status": "verified",
"target_action": "remove the stray set braces while retaining the absolute-value bars",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C024",
"native": {
"category": "mathematical_operator",
"evidence": "the expansion now matches its adjacent summation formula",
"file": "repo/source/sec_metric_space_summ.ptx",
"id": "O003-C024",
"source_issue": "the summary's expanded Euclidean-distance formula omits the plus sign before the final squared coordinate difference",
"source_locator": "authority line 53",
"status": "verified",
"target_action": "insert the missing plus sign",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C025",
"native": {
"category": "mathematical_domain",
"evidence": "the following open-ball definition remains general and d is used only on its declared domain X",
"file": "repo/source/sec_metric_space_exer.ptx",
"id": "O003-C025",
"source_issue": "the modular-metric exercise calls d a metric on R^2 even though d was defined only on X={1,3,5}",
"source_locator": "authority line 35",
"status": "verified",
"target_action": "state the unit-circle sentence as general motivation using a metric space such as R^2 rather than attributing d to R^2",
"unit": "chapter_03_metric_spaces"
}
},
{
"id": "O003-C026",
"native": {
"category": "open_ball_boundary",
"evidence": "B(b,r) was defined with d(y,b)0 and y<0 omit the x-axis but the prose says the y-axis is omitted",
"source_locator": "authority lines 357 and 360",
"status": "verified",
"target_action": "identify the omitted axis as the x-axis in both descriptions",
"unit": "chapter_13_closed_sets_in_topological_spaces"
}
},
{
"id": "O003-C157",
"native": {
"category": "mathematical_variable",
"evidence": "the repaired ambient set is fixed by the exercise introduction",
"file": "repo/source/sec_closed_sets_top_exer.ptx",
"id": "O003-C157",
"source_issue": "the discrete-line exercise asks for complements in an undefined ambient X although the entire exercise is in (Z,tau_dl)",
"source_locator": "authority lines 430 and 455",
"status": "verified",
"target_action": "write Z setminus closure(A) and Z setminus closure(B)",
"unit": "chapter_13_closed_sets_in_topological_spaces"
}
},
{
"id": "O003-C158",
"native": {
"category": "logical_scope",
"evidence": "this matches the cited point-to-set-distance exercise and supplies the useful closed-set characterization",
"file": "repo/source/sec_closed_sets_top_exer.ptx",
"id": "O003-C158",
"source_issue": "the metric regularity exercise assumes x lies outside C and then states d(x,C)=0 iff x lies in C, a contradictory restriction that erases the cited characterization",
"source_locator": "authority line 466",
"status": "verified",
"target_action": "for nonempty closed C quantify over every x in X before stating d(x,C)=0 iff x is in C",
"unit": "chapter_13_closed_sets_in_topological_spaces"
}
},
{
"id": "O003-C159",
"native": {
"category": "mathematical_notation",
"evidence": "the preceding and following occurrences identify the intended real line unambiguously",
"file": "repo/source/sec_closed_sets_top_exer.ptx",
"id": "O003-C159",
"source_issue": "the K-topology exercise uses the plain letter R rather than the real-number macro in one occurrence",
"source_locator": "authority line 502",
"status": "verified",
"target_action": "write (\\\\R,\\\\tau_K) consistently",
"unit": "chapter_13_closed_sets_in_topological_spaces"
}
},
{
"id": "O003-C160",
"native": {
"category": "logical_direction",
"evidence": "basis generation defines the topology; containment of the Euclidean basis proves the stated comparison in the correct direction",
"file": "repo/source/sec_closed_sets_top_exer.ptx",
"id": "O003-C160",
"source_issue": "the introduction says that B generates tau_K because tau_K is finer than the Euclidean topology, reversing the construction and its consequence",
"source_locator": "authority line 489",
"status": "verified",
"target_action": "state that B is a basis for tau_K and then infer fineness from B containing all ordinary open intervals",
"unit": "chapter_13_closed_sets_in_topological_spaces"
}
},
{
"id": "O003-C161",
"native": {
"category": "schema_structure",
"evidence": "the repair is reader-equivalent and makes the cumulative source conform to the frozen PreTeXt 1.7.5 RelaxNG model",
"file": "repo/source/sec_closed_sets_top_exer.ptx",
"id": "O003-C161",
"source_issue": "a definition block is nested inside a divisional-exercise introduction where the pinned PreTeXt schema permits paragraph-level introductory content but not a block definition",
"source_locator": "authority lines 253-261",
"status": "verified",
"target_action": "preserve the complete definition and index term as an explicitly labeled definition paragraph inside the same introduction",
"unit": "chapter_13_closed_sets_in_topological_spaces"
}
},
{
"id": "O003-C162",
"native": {
"category": "mathematical_notation",
"evidence": "the theorem and every adjacent occurrence identify the same inverse image unambiguously",
"file": "repo/source/sec_cont_top_intro.ptx",
"id": "O003-C162",
"source_issue": "the inverse-image expression is malformed as f^{-1}O), with a missing opening parenthesis",
"source_locator": "authority line 188",
"status": "verified",
"target_action": "write f^{-1}(O) consistently with the surrounding proof",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C163",
"native": {
"category": "mathematical_variable",
"evidence": "the task invokes a basis for the topology and the open-set characterization, so topology symbols are the exact structures in scope",
"file": "repo/source/sec_cont_top_intro.ptx",
"id": "O003-C163",
"source_issue": "the basis activity calls both spaces topological but denotes them by metric symbols (X,d_X) and (Y,d_Y), although no metrics are assumed",
"source_locator": "authority line 166",
"status": "verified",
"target_action": "write (X,\\\\tau_X) and (Y,\\\\tau_Y) in the translated activity",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C164",
"native": {
"category": "typographical",
"evidence": "the theorem statement and notation make the intended word certain and no mathematical content changes",
"file": "repo/source/sec_cont_top_intro.ptx",
"id": "O003-C164",
"source_issue": "topological is misspelled as topologicval in the closed-set characterization theorem",
"source_locator": "authority line 252",
"status": "verified",
"target_action": "use ruang topologi in the Indonesian derivative",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C165",
"native": {
"category": "schema_structure",
"evidence": "all definition text, index entries, mathematical content, and surrounding inquiry tasks are retained; only the invalid container and block position change",
"file": "repo/source/sec_cont_top_intro.ptx",
"id": "O003-C165",
"source_issue": "the formal open-function definition is nested inside a task statement, where the pinned PreTeXt schema does not permit a block definition",
"source_locator": "authority lines 111-129",
"status": "verified",
"target_action": "move the intact definition subtree to the section level immediately after the containing exploration",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C166",
"native": {
"category": "definition_consistency",
"evidence": "the repair reconciles adjacent statements without broadening the definition or changing the metric-equivalence criterion",
"file": "repo/source/sec_metric_equiv.ptx",
"id": "O003-C166",
"source_issue": "the prose calls any distance-preserving function an isometry while the immediately following formal definition requires a distance-preserving bijection",
"source_locator": "authority lines 86-100",
"status": "verified",
"target_action": "state in the prose that the function is bijective, preserving the book's explicit formal convention",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C167",
"native": {
"category": "mathematical_variable",
"evidence": "the definition concerns arbitrary topological spaces and therefore requires topology symbols rather than metric symbols",
"file": "repo/source/sec_top_equiv.ptx",
"id": "O003-C167",
"source_issue": "the definition calls (X,d_X) and (Y,d_Y) topological spaces although no metrics are assumed",
"source_locator": "authority line 17",
"status": "verified",
"target_action": "write (X,\\tau_X) and (Y,\\tau_Y) consistently with the immediately following homeomorphism definition",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C168",
"native": {
"category": "typographical",
"evidence": "the subject consists of the two spaces and the source's second to is an unambiguous grammatical slip",
"file": "repo/source/sec_top_equiv.ptx",
"id": "O003-C168",
"source_issue": "the homeomorphic-spaces sentence says the spaces (X,\\tau_X) to (Y,\\tau_Y) are homeomorphic",
"source_locator": "authority lines 50-53",
"status": "verified",
"target_action": "join the two named spaces with and in the Indonesian sentence",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C169",
"native": {
"category": "mathematical_exposition",
"evidence": "homeomorphisms need not be smooth or globally Lipschitz, while the immediately following theorem correctly proves that two-sided global Lipschitz bounds imply topological equivalence",
"file": "repo/source/sec_top_equiv.ptx",
"id": "O003-C169",
"source_issue": "the transition claims continuity of a homeomorphism ensures a smooth deformation and that metric distortion must be globally bounded",
"source_locator": "authority lines 60-69",
"status": "verified",
"target_action": "state that a homeomorphism preserves topological structure but need not be differentiably smooth or globally bi-Lipschitz; present two-sided distance bounds as the stronger sufficient condition proved next",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C170",
"native": {
"category": "typographical",
"evidence": "the following instruction to explain confirms the sentence is a question",
"file": "repo/source/sec_top_equiv.ptx",
"id": "O003-C170",
"source_issue": "the final activity uses awkward interrogative grammar and ends the question with a period",
"source_locator": "authority lines 136-139",
"status": "verified",
"target_action": "render it as a direct Indonesian question with a question mark",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C171",
"native": {
"category": "logical_scope",
"evidence": "the definition is intended as a relation on S and the added quantifier scope removes ambiguity without changing its meaning",
"file": "repo/source/sec_relations.ptx",
"id": "O003-C171",
"source_issue": "the symmetry and transitivity clauses say 'whenever ... in S' without explicitly quantifying the elements",
"source_locator": "authority lines 49-57",
"status": "verified",
"target_action": "state that the implications range over every relevant pair or triple of elements, while preserving the original math nodes and relation order",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C172",
"native": {
"category": "logical_scope",
"evidence": "an equivalence relation is defined on a set; the scoped wording prevents an unintended proper-class reading and preserves the requested proof task",
"file": "repo/source/sec_relations.ptx",
"id": "O003-C172",
"source_issue": "the two learner tasks call metric and topological equivalence an equivalence relation without naming the collection on which the relation is considered",
"source_locator": "authority lines 82-90",
"status": "verified",
"target_action": "scope each task to any chosen set of metric spaces or topological spaces",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C173",
"native": {
"category": "grammar",
"evidence": "the task compares two topological spaces and the plural wording removes an unambiguous number mismatch",
"file": "repo/source/sec_top_invar.ptx",
"id": "O003-C173",
"source_issue": "the activity asks whether X and Y are a singular homeomorphic space although it names two spaces",
"source_locator": "authority line 28",
"status": "verified",
"target_action": "render X and Y as homeomorphic spaces in the Indonesian activity",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C174",
"native": {
"category": "terminology_spelling",
"evidence": "indiskret is the established corpus term and the correction changes no mathematical content",
"file": "repo/source/sec_top_invar.ptx",
"id": "O003-C174",
"source_issue": "the Indonesian draft used indisret instead of the established Indonesian topology spelling indiskret",
"source_locator": "authority line 35",
"status": "verified",
"target_action": "normalize the learner task to topologi indiskret",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C175",
"native": {
"category": "grammar",
"evidence": "the source article is grammatically incorrect and the mathematical assertion is unchanged",
"file": "repo/source/sec_cont_top_summ.ptx",
"id": "O003-C175",
"source_issue": "the metric-equivalence summary says there is a isometry",
"source_locator": "authority line 20",
"status": "verified",
"target_action": "render the article-correct Indonesian sentence as terdapat isometri",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C176",
"native": {
"category": "grammar",
"evidence": "between requires the conjunction and; the correction preserves the intended pair of spaces",
"file": "repo/source/sec_cont_top_summ.ptx",
"id": "O003-C176",
"source_issue": "the topological-equivalence summary says there is a homeomorphism between X to Y",
"source_locator": "authority line 23",
"status": "verified",
"target_action": "render the relation as a homeomorphism antara X dan Y",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C177",
"native": {
"category": "grammar",
"evidence": "the repaired clause identifies X as the space possessing the property without changing the definition",
"file": "repo/source/sec_cont_top_summ.ptx",
"id": "O003-C177",
"source_issue": "the invariant summary omits the article in the phrase that topological space X has",
"source_locator": "authority line 34",
"status": "verified",
"target_action": "render the Indonesian clause as sifat yang dimiliki ruang topologi X",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C178",
"native": {
"category": "grammar",
"evidence": "the sentence names two spaces and the plural form removes an unambiguous number mismatch",
"file": "repo/source/sec_cont_top_exer.ptx",
"id": "O003-C178",
"source_issue": "the discrete-topology true/false statement says X and Y are topological space",
"source_locator": "authority line 557",
"status": "verified",
"target_action": "render the Indonesian statement with the plural ruang topologi",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C179",
"native": {
"category": "grammar",
"evidence": "the intended definition and the two cited exercises are explicit; the repair changes no topology or xref",
"file": "repo/source/sec_cont_top_exer.ptx",
"id": "O003-C179",
"source_issue": "the introduction begins with an ungrammatical fragment before defining the two point topologies and their status as topologies",
"source_locator": "authority lines 193-218",
"status": "verified",
"target_action": "render the Indonesian introduction as a complete definition and a factual cross-reference",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C180",
"native": {
"category": "grammar",
"evidence": "the mathematical map and source spaces are unchanged while the sentence becomes syntactically complete",
"file": "repo/source/sec_cont_top_exer.ptx",
"id": "O003-C180",
"source_issue": "the finite-complement true/false statement uses the fragment f(x)=x^2 mapping ... is continuous",
"source_locator": "authority lines 538-540",
"status": "verified",
"target_action": "render it as the map f(x)=x^2 from one named topological space to the other",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C181",
"native": {
"category": "terminology_consistency",
"evidence": "the terminology ledger and prior admitted chapters consistently use Euklides",
"file": "repo/source/sec_cont_top_exer.ptx",
"id": "O003-C181",
"source_issue": "the first Indonesian exercise draft used Euclides although the established corpus spelling is Euklides",
"source_locator": "translated lines 164 and 255-256",
"status": "verified",
"target_action": "normalize all three occurrences to topologi Euklides or topologi metrik Euklides",
"unit": "chapter_14_continuity_and_homeomorphisms"
}
},
{
"id": "O003-C182",
"native": {
"category": "logical_scope",
"evidence": "the correction removes an unstable display-label dependency and aligns the conclusion with both explicit nonempty hypotheses without changing the constructed topology",
"file": "repo/source/sec_sub.ptx",
"id": "O003-C182",
"source_issue": "the task conclusion refers to item (1) although no stable generated label is guaranteed and then says any subset despite the chapter's explicit nonempty-subspace convention",
"source_locator": "authority line 40",
"status": "verified",
"target_action": "refer to the result above and state every nonempty subset consistently with the adjacent exploration and formal definition",
"unit": "chapter_15_subspaces"
}
},
{
"id": "O003-C183",
"native": {
"category": "mathematical_notation",
"evidence": "the plain symbol is undefined in context; the repair restores the stated basis family without changing the proof task",
"file": "repo/source/sec_base_sub.ptx",
"id": "O003-C183",
"source_issue": "the basis-intersection task writes B in plain italic although the surrounding section defines and consistently uses the basis family macro \\\\B",
"source_locator": "authority line 40",
"status": "verified",
"target_action": "replace B by the established \\\\B macro in that membership expression",
"unit": "chapter_15_subspaces"
}
},
{
"id": "O003-C184",
"native": {
"category": "grammar",
"evidence": "the number repair preserves the exact intersection characterization",
"file": "repo/source/sec_sub_summ.ptx",
"id": "O003-C184",
"source_issue": "the singular subject a relatively closed set is paired with the plural predicate are the sets",
"source_locator": "authority line 21",
"status": "verified",
"target_action": "render the Indonesian summary with the singular form suatu himpunan tertutup relatif berbentuk A intersection C",
"unit": "chapter_15_subspaces"
}
},
{
"id": "O003-C185",
"native": {
"category": "schema_structure",
"evidence": "all figure content and the stable ID are retained; the new location is schema-valid and the xref remains resolved",
"file": "repo/source/sec_sub.ptx",
"id": "O003-C185",
"source_issue": "the raster figure is nested inside an exploration introduction where the pinned PreTeXt schema does not admit that figure model or an accessibility description",
"source_locator": "authority lines 28-35",
"status": "verified",
"target_action": "move the complete figure block to section level immediately before the exploration and add a faithful Indonesian description",
"unit": "chapter_15_subspaces"
}
},
{
"id": "O003-C186",
"native": {
"category": "schema_structure",
"evidence": "the stable ID index definition statement and mathematics are unchanged while the source becomes schema-valid",
"file": "repo/source/sec_sub.ptx",
"id": "O003-C186",
"source_issue": "a formal definition is nested inside a task statement where the pinned PreTeXt schema does not admit it",
"source_locator": "authority lines 43-55",
"status": "verified",
"target_action": "move the complete definition block to section level immediately after the exploration",
"unit": "chapter_15_subspaces"
}
},
{
"id": "O003-C187",
"native": {
"category": "schema_structure",
"evidence": "all reader-facing definition content terminology mathematics and the exercise prompt remain in order while the chapter validates",
"file": "repo/source/sec_sub_exer.ptx",
"id": "O003-C187",
"source_issue": "a formal definition and its statement shell are nested inside an exercise statement where the pinned PreTeXt schema does not admit them",
"source_locator": "authority lines 89-97",
"status": "verified",
"target_action": "remove only the two invalid ancestor shells retain the index entry in the introductory paragraph and retain the defining paragraph as the next paragraph of the same exercise statement",
"unit": "chapter_15_subspaces"
}
},
{
"id": "O003-C188",
"native": {
"category": "terminology_typo",
"evidence": "module is an unambiguous typographical substitution; the correction restores the standard relation without changing any formula",
"file": "repo/source/sec_quotients.ptx",
"id": "O003-C188",
"source_issue": "the English source says congruence module n although the established arithmetic relation is congruence modulo n",
"source_locator": "authority line 18",
"status": "verified",
"target_action": "render the Indonesian sentence as relasi kongruensi modulo n",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C189",
"native": {
"category": "mathematical_object",
"evidence": "the surrounding sentences and section title unambiguously define the quotient topology; no function is being introduced at that point",
"file": "repo/source/sec_quotient_top.ptx",
"id": "O003-C189",
"source_issue": "the English source calls the resulting object on Y a function although the construction defines a topology",
"source_locator": "authority line 4",
"status": "verified",
"target_action": "render the object correctly as topologi yang dihasilkan pada Y",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C190",
"native": {
"category": "equivalence_relation_scope",
"evidence": "equivalence closure is required for the claimed quotient construction and preserves every displayed generating identification",
"file": "repo/source/sec_quotient_space.ptx",
"id": "O003-C190",
"source_issue": "the listed ordered identifications do not literally include all reflexive symmetric and transitive pairs even though the source calls the result an equivalence relation",
"source_locator": "authority lines 211-214 and 259-308",
"status": "verified",
"target_action": "state that the equivalence relation is generated by the displayed identifications",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C191",
"native": {
"category": "mathematical_notation",
"evidence": "the frozen figure stem Mobius_identification and its opposite arrows unambiguously pair the bottom edge with the top edge in reverse direction; the adjacent parts likewise correspond in order to Torus_identification and Quotient_sphere_1",
"file": "repo/source/sec_quotient_space.ptx",
"id": "O003-C191",
"source_issue": "part (i) identifies the bottom edge with itself by (x,0) equivalent to (1-x,0) although its first diagram is the Möbius identification of opposite edges",
"source_locator": "authority line 270",
"status": "verified",
"target_action": "replace the second endpoint by (1-x,1)",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C192",
"native": {
"category": "mathematical_object",
"evidence": "the displayed relations and the paired Mobius_identification and Torus_identification figures unambiguously define the standard square quotient models in that order",
"file": "repo/source/sec_quotient_space.ptx",
"id": "O003-C192",
"source_issue": "part (ii) identifies both pairs of opposite square edges in matching directions and all four corners but calls the resulting space a Möbius strip",
"source_locator": "authority lines 275 and 283",
"status": "verified",
"target_action": "restore the Möbius name and index to corrected part (i) and index and name part (ii) as a torus",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C193",
"native": {
"category": "mathematical_scope",
"evidence": "the quotient is not literally the closed interval; this wording preserves the intended fundamental-domain construction",
"file": "repo/source/sec_find_quotient_space.ptx",
"id": "O003-C193",
"source_issue": "the source says the equivalence relation identifies the real line with the interval [0,1] although the interval only supplies representatives and its endpoints are identified",
"source_locator": "authority lines 26-27",
"status": "verified",
"target_action": "state that every equivalence class has a representative in [0,1] with the two endpoints identified",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C194",
"native": {
"category": "mathematical_notation",
"evidence": "the immediately preceding display defines S^1 and no object S_1 is defined",
"file": "repo/source/sec_find_quotient_space.ptx",
"id": "O003-C194",
"source_issue": "the objective names the unit circle as S_1 although the defining display and every subsequent occurrence use S^1",
"source_locator": "authority line 30",
"status": "verified",
"target_action": "replace S_1 by S^1",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C195",
"native": {
"category": "ambient_space_error",
"evidence": "the corrected identity is type-consistent and directly proves continuity of the induced map",
"file": "repo/source/sec_find_quotient_space.ptx",
"id": "O003-C195",
"source_issue": "the proof equates a subset of X with the inverse image under the induced map which is a subset of X/~ and then calls that subset open in X",
"source_locator": "authority lines 139-148",
"status": "verified",
"target_action": "replace the invalid chain by f^{-1}(O)=p^{-1}(overline f^{-1}(O)) and apply the quotient-topology criterion in X/~",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C196",
"native": {
"category": "period_error",
"evidence": "the period in the variable t is 1 so the preimage components are (A+k,B+k) for integers k",
"file": "repo/source/sec_find_quotient_space.ptx",
"id": "O003-C196",
"source_issue": "for f(t)=(cos(2 pi t),sin(2 pi t)) the source translates lifted intervals by 2 pi k and calls A and B angles",
"source_locator": "authority lines 190-194",
"status": "verified",
"target_action": "treat A and B as normalized real parameters and translate the lifted intervals by k",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C197",
"native": {
"category": "proof_scope",
"evidence": "such subintervals cover O and their images cover f(O), proving that f is open without the overbroad interval claim",
"file": "repo/source/sec_find_quotient_space.ptx",
"id": "O003-C197",
"source_issue": "the source claims every interval contained in O maps to the single endpoint-determined open arc although an interval of length at least 1 can wrap around the circle",
"source_locator": "authority lines 237-242",
"status": "verified",
"target_action": "choose around every point an open subinterval of length less than 1 and take the union of its open-arc images",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C198",
"native": {
"category": "mathematical_object",
"evidence": "p is the surjective function in the preceding bullet while the quotient topology is the displayed family of subsets of Y",
"file": "repo/source/sec_quotients_summ.ptx",
"id": "O003-C198",
"source_issue": "the source calls the function p a quotient topology and the resulting sentence is grammatically malformed",
"source_locator": "authority line 18",
"status": "verified",
"target_action": "state that p in the preceding construction is called a quotient map and Y is called a quotient space",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C199",
"native": {
"category": "empty_subspace_edge_case",
"evidence": "the corrected formula gives the intended collapse quotient for every subspace and explicitly leaves the empty-subspace case unchanged",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C199",
"source_issue": "the claimed equivalence classes include A itself even when A is empty although an empty set cannot be an equivalence class and the intuition then says the empty set is collapsed to a point",
"source_locator": "authority lines 59-62",
"status": "verified",
"target_action": "define x equivalent to y exactly when x equals y or both points belong to A and qualify the collapse intuition so the empty case creates no point",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C200",
"native": {
"category": "underdetermined_equivalence_relations",
"evidence": "equivalence closure supplies symmetry and transitivity while the coordinate formula removes geometric ambiguity without adding identifications",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C200",
"source_issue": "reflexivity alone does not fully specify the equivalence closure of the stated identifications and diagonally opposite is ambiguous for disk points",
"source_locator": "authority lines 134-158",
"status": "verified",
"target_action": "declare the equivalence relation generated by exactly the stated identifications and express the antipodal condition as y=-x",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C201",
"native": {
"category": "underdetermined_equivalence_relation",
"evidence": "the biconditional is reflexive on the base edge and makes every positive horizontal slice one equivalence class",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C201",
"source_issue": "the wording separately supplies a positive-height condition and reflexivity but does not explicitly state the complete binary relation",
"source_locator": "authority lines 167-170",
"status": "verified",
"target_action": "state that two points are equivalent exactly when they are equal or have the same positive second coordinate",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C202",
"native": {
"category": "mathematical_notation",
"evidence": "the corrected symbol matches the definition in the same exercise and the established notation throughout the book",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C202",
"source_issue": "the excluded-point topology is written with a duplicated nested tau subscript",
"source_locator": "authority line 231",
"status": "verified",
"target_action": "replace tau sub tau sub overline p by tau sub overline p",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C203",
"native": {
"category": "projective_geometry_error",
"evidence": "this is the incidence structure of the real projective plane defined immediately afterward",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C203",
"source_issue": "the source posits one point at infinity where all lines intersect although projective completion adds one ideal point for each parallel direction",
"source_locator": "authority lines 241-250",
"status": "verified",
"target_action": "state that distinct projective lines meet once and parallel affine lines of one direction share their corresponding point at infinity",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C204",
"native": {
"category": "mathematical_notation",
"evidence": "the adjacent occurrences at authority lines 274 and 288 use the intended quotient notation",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C204",
"source_issue": "one quotient occurrence uses the ordinary relation macro after the book introduced its spaced quotient-relation macro",
"source_locator": "authority line 284",
"status": "verified",
"target_action": "replace S^2 slash sim by S^2 slash ssim",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C205",
"native": {
"category": "mathematical_notation",
"evidence": "every other occurrence in the exercise uses mathbb R P^2",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C205",
"source_issue": "one real-projective-plane occurrence uses bold R rather than blackboard-bold R",
"source_locator": "authority line 347",
"status": "verified",
"target_action": "replace mathbf R P^2 by mathbb R P^2",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C206",
"native": {
"category": "classification_scope",
"evidence": "the corrected alternatives are the standard classification boundary and avoid treating disconnected surfaces or ordinary unions as connected sums",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C206",
"source_issue": "the informal statement says every closed surface is made from spheres tori and projective planes without connectedness or the connected-sum classification",
"source_locator": "authority lines 313-315",
"status": "verified",
"target_action": "state the connected closed-surface classification as the sphere a finite connected sum of tori or a finite connected sum of real projective planes",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C207",
"native": {
"category": "lexical_mathematical_error",
"evidence": "the surrounding definition requires a continuous map and the corrected adverb expresses that property",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C207",
"source_issue": "the source says continually collapse where continuity of the deformation is intended",
"source_locator": "authority line 408",
"status": "verified",
"target_action": "state continuously collapse",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C208",
"native": {
"category": "duplicate_prompts_retained",
"evidence": "the repetition is byte-identical and there is no primary evidence for intended replacement questions; transparent aliasing avoids silently inventing or deleting source content",
"file": "repo/source/sec_quotients_exer.ptx",
"id": "O003-C208",
"source_issue": "the first two true-or-false prompts are repeated verbatim as the third and fourth prompts",
"source_locator": "authority lines 456-489",
"status": "verified",
"target_action": "retain both source occurrences to preserve exercise topology and map the later copies as explicit backend aliases of the first pair",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C209",
"native": {
"category": "build_configuration",
"evidence": "the pinned authority defines the macro globally and Chapter 16 uses it throughout; restoring that lossless definition preserves source notation and closes the strict build dependency",
"file": "repo/source/chapters_01_16_reader.ptx",
"id": "O003-C209",
"source_issue": "the cumulative reader wrapper omitted the source-defined quotient-relation macro ssim, causing the strict XeLaTeX build to stop at the first quotient-space occurrence",
"source_locator": "authority source/main.ptx line 83",
"status": "verified",
"target_action": "restore the exact upstream definition newcommand ssim equals sim in the cumulative wrapper macro block",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C210",
"native": {
"category": "build_configuration",
"evidence": "the companion's unit-circle description uses the conventional complex-number set and the pinned authority provides this exact lossless macro definition",
"file": "repo/source/chapters_01_16_reader.ptx",
"id": "O003-C210",
"source_issue": "the cumulative reader wrapper omitted the source-defined complex-number macro C used by the original Chapter 16 self-study companion",
"source_locator": "authority source/main.ptx line 13",
"status": "verified",
"target_action": "restore the exact upstream definition newcommand C equals mathbb C in the cumulative wrapper macro block",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C211",
"native": {
"category": "build_configuration",
"evidence": "the local definition retains every source math token and gives both MathJax and XeLaTeX conventional arc notation without importing unicode-math and globally changing the established cumulative reader fonts or pagination; all four final uses receive targeted visual QA",
"file": "repo/source/chapters_01_16_reader.ptx",
"id": "O003-C211",
"source_issue": "the cumulative derivative wrapper omitted the upstream unicode-math preamble that supplies overparen, causing strict XeLaTeX failure at the four retained open-arc expressions",
"source_locator": "authority source/main.ptx lines 171-174 and source/sec_find_quotient_space.ptx lines 189-194 and 239",
"status": "verified",
"target_action": "define overparen locally with one argument as overset frown over that argument in the cumulative wrapper macro block",
"unit": "chapter_16_quotient_spaces"
}
},
{
"id": "O003-C212",
"native": {
"category": "grammar",
"evidence": "the surrounding construction and both adjacent uses unambiguously require the verb cover with no preposition",
"file": "repo/source/sec_compact_top_intro.ptx",
"id": "O003-C212",
"source_issue": "the source phrase collections of open sets that cover of (0,1) contains an extraneous of",
"source_locator": "authority line 67",
"status": "verified",
"target_action": "translate the intended statement as collections of open sets that cover (0,1)",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C213",
"native": {
"category": "mathematical_reference",
"evidence": "the immediately preceding paragraph explicitly constructs the extended cover by adjoining O0 and O1 and the three stated sets then cover [0,1]",
"file": "repo/source/sec_compact_top_intro.ptx",
"id": "O003-C213",
"source_issue": "O0 O1 and O4 are called a finite subcover of the family {On} indexed by n at least 3 even though O0 and O1 are not members of that family",
"source_locator": "authority lines 120-121",
"status": "verified",
"target_action": "identify them as a finite subcover of the previously described cover extended by O0 and O1",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C214",
"native": {
"category": "missing_hypothesis",
"evidence": "the book defines a topological space as any set carrying a topology so the empty space is allowed; nonemptiness makes f(X) nonempty and the least-upper-bound argument valid",
"file": "repo/source/sec_compact_app.ptx",
"id": "O003-C214",
"source_issue": "the maximum-minimum claim permits the empty compact topological space even though a function with empty domain has no attained maximum or minimum",
"source_locator": "authority lines 4 and 16 plus downstream summary",
"status": "verified",
"target_action": "state the theorem and its proof activity for a nonempty compact topological space and propagate the same scope to the chapter summary",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C215",
"native": {
"category": "undefined_map",
"evidence": "the preceding theorem proves preservation under continuous maps and applying it to a named homeomorphism and its inverse gives the asserted equivalence",
"file": "repo/source/sec_compact_cont.ptx",
"id": "O003-C215",
"source_issue": "the corollary refers to f(A) after saying only that X and Y are homeomorphic and never introduces f",
"source_locator": "authority lines 135-139",
"status": "verified",
"target_action": "state in prose that f is a homeomorphism from the displayed space X to the displayed space Y",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C216",
"native": {
"category": "index_domain",
"evidence": "Q_0 is the initial cube and the inductive construction defines Q_k only for subsequent nonnegative indices",
"file": "repo/source/sec_compact_rn.ptx",
"id": "O003-C216",
"source_issue": "the nested-cube proof quantifies k over all integers although only cubes with nonnegative indices are constructed",
"source_locator": "authority line 187",
"status": "verified",
"target_action": "restrict k to the nonnegative integers",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C217",
"native": {
"category": "mathematical_notation",
"evidence": "an n-dimensional cube is the product of all n displayed closed intervals",
"file": "repo/source/sec_compact_rn.ptx",
"id": "O003-C217",
"source_issue": "the Cartesian-product display omits the multiplication sign before its final interval factor",
"source_locator": "authority line 194",
"status": "verified",
"target_action": "insert the missing Cartesian-product times sign before the final factor",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C218",
"native": {
"category": "proof_gap",
"evidence": "for j below i monotonicity gives a_j_s no greater than a_i_s no greater than b_i_s and for j above i containment Q_j in Q_i gives a_j_s no greater than b_i_s",
"file": "repo/source/sec_compact_rn.ptx",
"id": "O003-C218",
"source_issue": "the proof cites only a_i_s less than or equal to b_i_s to conclude that the supremum of all a_i_s is below every b_i_s",
"source_locator": "authority lines 217-223",
"status": "verified",
"target_action": "use nesting explicitly to show that each b_i_s is an upper bound for every a_j_s before applying the least-upper-bound property",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C219",
"native": {
"category": "strictness_error",
"evidence": "equality can hold at an opposite corner and the corrected chain still places Q_K inside the epsilon ball",
"file": "repo/source/sec_compact_rn.ptx",
"id": "O003-C219",
"source_issue": "D_K is defined as the maximum distance in Q_K but the source asserts every point has distance strictly below D_K",
"source_locator": "authority lines 247-248",
"status": "verified",
"target_action": "use d_E(q,x) less than or equal to D_K less than epsilon_q",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C220",
"native": {
"category": "dimension_index",
"evidence": "m counts the chosen finite subcover while n is the dimension fixed throughout the proof",
"file": "repo/source/sec_compact_rn.ptx",
"id": "O003-C220",
"source_issue": "the final Heine-Borel containment uses Q_K to the power m although the ambient Euclidean dimension is n",
"source_locator": "authority line 359",
"status": "verified",
"target_action": "replace Q_K^m by Q_K^n",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C221",
"native": {
"category": "duplicate_prompt_retained",
"evidence": "there is no primary evidence for a missing replacement prompt so transparent aliasing preserves source topology without inventing work",
"file": "repo/source/sec_compact_top_exer.ptx",
"id": "O003-C221",
"source_issue": "the first exercise contains two byte-identical tasks",
"source_locator": "authority lines 3-18",
"status": "verified",
"target_action": "retain both physical occurrences and map the second as an explicit backend alias of the first",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C222",
"native": {
"category": "wrong_ambient_set",
"evidence": "all preceding tasks and the stated topology concern the fixed underlying set X and no topology on the integers is defined",
"file": "repo/source/sec_compact_top_exer.ptx",
"id": "O003-C222",
"source_issue": "the Either-Or exercise defines X as the interval [-1,1] but its last task asks about subsets of the integers",
"source_locator": "authority lines 190-223",
"status": "verified",
"target_action": "ask about subsets of X",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C223",
"native": {
"category": "missing_hypothesis",
"evidence": "the requested disjoint neighborhoods are impossible when x belongs to A and the corrected statement is the standard compact-set separation theorem",
"file": "repo/source/sec_compact_top_exer.ptx",
"id": "O003-C223",
"source_issue": "the Hausdorff separation task permits x to belong to the compact set A while requiring disjoint open sets containing x and A",
"source_locator": "authority lines 374-381",
"status": "verified",
"target_action": "require x to lie in X minus A",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C224",
"native": {
"category": "unbound_variable",
"evidence": "the neighborhood must contain the point quantified at the beginning of the definition",
"file": "repo/source/sec_compact_top_exer.ptx",
"id": "O003-C224",
"source_issue": "the local-compactness definition quantifies x but requires the undefined point p to lie in O",
"source_locator": "authority lines 433-438",
"status": "verified",
"target_action": "replace p in O by x in O",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C225",
"native": {
"category": "incorrect_affine_map",
"evidence": "the corrected map sends v_i to itself and sends every x to the midpoint of x and v_i exactly as the construction requires",
"file": "repo/source/sec_fractals.ptx",
"id": "O003-C225",
"source_issue": "the stated half-scale affine map adds v_i rather than one half v_i even though the prose says v_i is fixed and every image point is the midpoint with v_i",
"source_locator": "authority lines 140-151",
"status": "verified",
"target_action": "replace the translation vector by one half v_i and describe the scale factor as one half",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C226",
"native": {
"category": "grammar",
"evidence": "denote by is the unambiguous grammatical construction naming the hyperspace",
"file": "repo/source/sec_fractals.ptx",
"id": "O003-C226",
"source_issue": "the source says the collection is denote at H(X)",
"source_locator": "authority line 116",
"status": "verified",
"target_action": "translate the intended phrase as denoted by H(X)",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C227",
"native": {
"category": "pretext_structure",
"evidence": "the repaired section preserves the inquiry order and validates with zero diagnostics in the cumulative Chapters 1-17 context",
"file": "repo/source/sec_compact_cont.ptx",
"id": "O003-C227",
"source_issue": "the compact-image theorem is nested inside the final activity task statement and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 115-132",
"status": "verified",
"target_action": "move the unchanged theorem to section level immediately after the activity while retaining the task prompt in place",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C228",
"native": {
"category": "pretext_structure",
"evidence": "the repaired section preserves the inquiry order and validates with zero diagnostics in the cumulative Chapters 1-17 context",
"file": "repo/source/sec_compact_rn.ptx",
"id": "O003-C228",
"source_issue": "the closed-subset-of-a-compact-space theorem is nested inside the final activity task statement and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 321-339",
"status": "verified",
"target_action": "move the unchanged theorem to section level immediately after the activity while retaining the task prompt in place",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C229",
"native": {
"category": "pretext_structure",
"evidence": "the theorem remains immediately adjacent to its proof activity and the cumulative Chapters 1-17 source validates with zero diagnostics",
"file": "repo/source/sec_compact_app.ptx",
"id": "O003-C229",
"source_issue": "the maximum-minimum theorem is nested inside an activity introduction and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 4-16",
"status": "verified",
"target_action": "move the theorem to section level before the activity and make the introduction explicitly identify the following activity as its proof",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C230",
"native": {
"category": "pretext_structure",
"evidence": "the repaired section preserves the inquiry sequence and prompt denominator and validates with zero diagnostics in the cumulative Chapters 1-17 context",
"file": "repo/source/sec_fractals.ptx",
"id": "O003-C230",
"source_issue": "the Hausdorff-distance definition and theorem are nested inside task statements in one activity and are invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 66-164",
"status": "verified",
"target_action": "split the activity into three consecutive activities and move the unchanged formal definition and theorem to section level at their original reading positions while retaining all four prompts",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C231",
"native": {
"category": "pretext_structure",
"evidence": "all chapter content remains present in the same topical neighborhood and the cumulative Chapters 1-17 source validates with zero diagnostics",
"file": "repo/source/chap_Compact_topology.ptx",
"id": "O003-C231",
"source_issue": "the source places a supplemental fractals section after the chapter divisional-exercises block although the pinned PreTeXt schema requires divisional exercises to be final",
"source_locator": "authority XInclude order",
"status": "verified",
"target_action": "place the unchanged fractals section immediately before the final exercises include",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C232",
"native": {
"category": "pretext_structure",
"evidence": "no mathematical content or prompt is removed and the cumulative Chapters 1-17 source validates with zero diagnostics",
"file": "repo/source/sec_compact_top_exer.ptx",
"id": "O003-C232",
"source_issue": "a formal local-compactness definition is nested inside a divisional-exercise introduction and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 433-441",
"status": "verified",
"target_action": "retain the complete definition and index term as an explicitly labeled definition paragraph in the same introduction",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C233",
"native": {
"category": "build_closure",
"evidence": "the strict PDF gate exposed the hidden partial build; the restored macro preserves every Chapter 17 source and companion expression and is required for a complete deterministic PDF",
"file": "repo/source/chapters_01_17_reader.ptx",
"id": "O003-C233",
"source_issue": "the cumulative derivative wrapper omitted the upstream definition \\\\newcommand{\\\\E}{\\\\mathbb{E}} although Chapter 17 exercises use \\\\E repeatedly; XeLaTeX therefore emitted an undefined-control-sequence error and only a partial PDF",
"source_locator": "authority main.ptx macro closure / derivative wrapper macros",
"status": "verified",
"target_action": "restore the exact upstream \\\\E macro definition in the cumulative reader wrapper",
"unit": "chapter_17_compact_spaces"
}
},
{
"id": "O003-C234",
"native": {
"category": "source_typo",
"evidence": "the correction changes no mathematical definition or XML topology and preserves the evident meaning of the surrounding path-connectedness paragraph",
"file": "repo/source/sec_path_intro.ptx",
"id": "O003-C234",
"source_issue": "the phrase 'from one point in the spaced to another' uses 'spaced' where the sentence unambiguously requires 'space'",
"source_locator": "authority line 10",
"status": "verified",
"target_action": "render the intended phrase naturally as 'dari satu titik ke titik lain dalam ruang tersebut'",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C235",
"native": {
"category": "pretext_structure",
"evidence": "the theorem's complete subtree and xml:id thm_connected_invariant are unchanged; only its invalid parent is repaired, and the cumulative Chapters 1-18 schema gate reports zero diagnostics",
"file": "repo/source/sec_connect_sets.ptx",
"id": "O003-C235",
"source_issue": "the connected-image theorem is nested inside the final task statement of an activity and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 171-187",
"status": "verified",
"target_action": "retain the task's explanatory prompt in place and hoist the unchanged theorem to section level immediately after the activity",
"unit": "chapter_18_connected_spaces"
}
},
{
"id": "O003-C236",
"native": {
"category": "pretext_structure",
"evidence": "the lemma's complete subtree and xml:id lem_separation_subset are unchanged; only its invalid parent is repaired, and the cumulative Chapters 1-18 schema gate reports zero diagnostics",
"file": "repo/source/sec_connect_subset_rn.ptx",
"id": "O003-C236",
"source_issue": "the separation lemma is nested inside the final task statement of an activity and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 41-58",
"status": "verified",
"target_action": "retain the task's proof prompt in place and hoist the unchanged lemma to section level immediately after the activity",
"unit": "chapter_18_connected_spaces"
}
},
{
"id": "O003-C237",
"native": {
"category": "pretext_structure",
"evidence": "the theorem remains immediately adjacent to its proof activity, all mathematical content is retained, and the cumulative Chapters 1-18 schema gate reports zero diagnostics",
"file": "repo/source/sec_ivt_fpt.ptx",
"id": "O003-C237",
"source_issue": "the fixed-point theorem is nested inside an activity introduction and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 77-96",
"status": "verified",
"target_action": "hoist the unchanged theorem to section level immediately before the activity while retaining the introduction's proof lead and hypotheses",
"unit": "chapter_18_connected_spaces"
}
},
{
"id": "O003-C238",
"native": {
"category": "pretext_structure",
"evidence": "no mathematical content or exercise prompt is removed; only the invalid definition and statement shells are flattened, and the cumulative Chapters 1-18 schema gate reports zero diagnostics",
"file": "repo/source/sec_connect_top_exer.ptx",
"id": "O003-C238",
"source_issue": "an un-IDed formal definition of local connectedness is nested inside a divisional-exercise introduction and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 153-170",
"status": "verified",
"target_action": "retain the complete index term and definition text as a paragraph explicitly labeled Definisi in the same introduction",
"unit": "chapter_18_connected_spaces"
}
},
{
"id": "O003-C239",
"native": {
"category": "pretext_structure",
"evidence": "the complete theorem subtree and xml:id thm_path_connected are preserved; only its invalid parent is repaired, and the isolated Chapter 19 schema gate reports zero diagnostics",
"file": "repo/source/sec_path_connect.ptx",
"id": "O003-C239",
"source_issue": "the path-connected-implies-connected theorem is nested inside an activity introduction and is invalid under the pinned PreTeXt schema",
"source_locator": "authority theorem thm_path_connected",
"status": "verified",
"target_action": "hoist the unchanged theorem to section level immediately before the activity while retaining the activity as its proof inquiry",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C240",
"native": {
"category": "pretext_structure",
"evidence": "the original prompt-before-definition reading order and physical prompt carrier are preserved, and the isolated Chapter 19 schema gate reports zero diagnostics",
"file": "repo/source/sec_path_connect_equiv.ptx",
"id": "O003-C240",
"source_issue": "the formal definition of the product of two paths is nested directly inside an activity and is invalid under the pinned PreTeXt schema",
"source_locator": "authority path-product definition",
"status": "verified",
"target_action": "move the unchanged definition to section level immediately after the activity and retain the activity's direct prompt paragraph referring to the following definition",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C241",
"native": {
"category": "pretext_structure",
"evidence": "no mathematical content or prompt is removed; only the invalid definition shell is flattened, and the isolated Chapter 19 schema gate reports zero diagnostics",
"file": "repo/source/sec_connect_finite.ptx",
"id": "O003-C241",
"source_issue": "the formal minimal-neighborhood definition is nested inside a task statement and is invalid under the pinned PreTeXt schema",
"source_locator": "authority definition def_min_nghb",
"status": "verified",
"target_action": "retain the complete index term, xml:id def_min_nghb, and definition text as an explicitly labeled paragraph inside the same task statement",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C242",
"native": {
"category": "variable_reference",
"evidence": "the corrected reference matches the quantified point and the following membership statement without changing the proof's argument",
"file": "repo/source/sec_connect_finite.ptx",
"id": "O003-C242",
"source_issue": "the proof refers to the neighborhood O of x even though it has just selected the point p and the next sentence uses p in O",
"source_locator": "authority lemma proof after selecting p in P",
"status": "verified",
"target_action": "render O as a neighborhood of p",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C243",
"native": {
"category": "grammar",
"evidence": "the correction is grammatical and preserves the quantified neighborhood and point",
"file": "repo/source/sec_connect_finite.ptx",
"id": "O003-C243",
"source_issue": "the source says 'any neighborhood of N of x', with an extraneous 'of' before N",
"source_locator": "authority minimal-neighborhood proof",
"status": "verified",
"target_action": "render the intended phrase as 'any neighborhood N of x'",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C244",
"native": {
"category": "mathematical_logic",
"evidence": "the repaired argument proves the stated converse and uses exactly the theorem's hypotheses",
"file": "repo/source/sec_connect_finite.ptx",
"id": "O003-C244",
"source_issue": "the reverse implication assumes that X is path connected and repeats the forward direction instead of proving that connectedness plus equality of components and path components implies path connectedness",
"source_locator": "authority final theorem reverse implication",
"status": "verified",
"target_action": "assume X is connected, use its single component C=X and the equality of components and path components, then conclude that X is path connected",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C245",
"native": {
"category": "formula_parenthesis",
"evidence": "the repaired expression is syntactically balanced and leaves every mathematical symbol and argument unchanged",
"file": "repo/source/sec_connect_infinite.ptx",
"id": "O003-C245",
"source_issue": "the displayed Euclidean-distance expression lacks the closing parenthesis that pairs with the opening delimiter around its two point arguments",
"source_locator": "authority distance display in connectedness proof",
"status": "verified",
"target_action": "restore the missing closing parenthesis after the second point",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C246",
"native": {
"category": "formula_reference",
"evidence": "the corrected point lies in B by its definition and is the same point used in the preceding distance estimate",
"file": "repo/source/sec_connect_infinite.ptx",
"id": "O003-C246",
"source_issue": "the proof concludes that (z,arcsin(z)) lies in the graph B although B is the graph of sin(1/x) and the constructed point has second coordinate sin(1/z)",
"source_locator": "authority connectedness proof constructed point",
"status": "verified",
"target_action": "render the constructed point as (z,sin(1/z))",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C247",
"native": {
"category": "punctuation",
"evidence": "the repair restores balanced punctuation without altering the mathematical claim",
"file": "repo/source/sec_connect_infinite.ptx",
"id": "O003-C247",
"source_issue": "the source opens a parenthetical with '(In fact,' at the end of the proof but never closes it",
"source_locator": "authority final proof sentence",
"status": "verified",
"target_action": "close the parenthetical at the end of the sentence",
"unit": "chapter_19_path_connected_spaces"
}
},
{
"id": "O003-C300",
"native": {
"category": "grammar",
"evidence": "the Indonesian question is grammatical and asks for the same smallest added collection",
"file": "repo/source/sec_prod_top.ptx",
"id": "O003-C300",
"source_issue": "the question says 'what is the smallest collection of sets would we need'",
"source_locator": "authority line 53",
"status": "verified",
"target_action": "render the intended question without the extraneous auxiliary construction",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C301",
"native": {
"category": "notation_consistency",
"evidence": "the corrected subscript matches every subsequent use in the basis construction",
"file": "repo/source/sec_top_prod_space.ptx",
"id": "O003-C301",
"source_issue": "the first factor is written (X tau) although the section consistently names its topology tau_X",
"source_locator": "authority line 16",
"status": "verified",
"target_action": "render the first factor as (X tau_X)",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C302",
"native": {
"category": "ambient_space",
"evidence": "both intervals are subsets of the real line and their product is then identified with the rectangle in R^2",
"file": "repo/source/sec_prod_top_exam.ptx",
"id": "O003-C302",
"source_issue": "the real intervals [1,2] and [3,4] are described as subspaces of R^2",
"source_locator": "authority line 10",
"status": "verified",
"target_action": "render them as subspaces of R",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C303",
"native": {
"category": "grammar",
"evidence": "the repaired number agreement preserves the described relatively open arc",
"file": "repo/source/sec_prod_top_exam.ptx",
"id": "O003-C303",
"source_issue": "the source says V is 'the intersections' of S^1 with an open ball",
"source_locator": "authority line 68",
"status": "verified",
"target_action": "render V as the singular intersection",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C304",
"native": {
"category": "formula_reference",
"evidence": "every repaired reference now lies in the declared radius-two first factor while the second factor remains S^1",
"file": "repo/source/sec_prod_top_exam.ptx",
"id": "O003-C304",
"source_issue": "the radius-two-circle activity repeatedly substitutes S^1 and unit-circle sample points for its declared first factor 2S^1",
"source_locator": "authority lines 75-116",
"status": "verified",
"target_action": "use p in 2S^1; S^1_p as a subset of 2S^1 times S^1; graph the first factor 2S^1; use sample points (2,0) (sqrt(2),sqrt(2)) and (0,2); and take U from 2S^1",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C305",
"native": {
"category": "grammar",
"evidence": "the quantified finite product has multiple topological-space factors",
"file": "repo/source/sec_proj_cont_prod.ptx",
"id": "O003-C305",
"source_issue": "the source says 'a product of topological space'",
"source_locator": "authority line 87",
"status": "verified",
"target_action": "render the plural 'ruang-ruang topologi'",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C306",
"native": {
"category": "pretext_structure",
"evidence": "the theorem ID and forward xref are preserved and isolated Chapter 20 schema validation reports zero diagnostics",
"file": "repo/source/sec_proj_cont_prod.ptx",
"id": "O003-C306",
"source_issue": "the theorem thm_subbasis_continuous is nested inside an activity statement and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 130-152",
"status": "verified",
"target_action": "move the unchanged theorem to section level immediately after the activity while retaining the direct proof prompt and hint",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C307",
"native": {
"category": "formula_parenthesis",
"evidence": "the repaired expression has balanced function arguments and states the standard inverse-image identity",
"file": "repo/source/sec_proj_cont_prod.ptx",
"id": "O003-C307",
"source_issue": "the inverse-image identity lacks the final closing parenthesis in g^{-1}(h^{-1}(O))",
"source_locator": "authority line 166",
"status": "verified",
"target_action": "restore the missing closing parenthesis",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C308",
"native": {
"category": "pretext_structure",
"evidence": "the theorem remains adjacent to the generating activity and isolated Chapter 20 schema validation reports zero diagnostics",
"file": "repo/source/sec_prop_prod_top.ptx",
"id": "O003-C308",
"source_issue": "the Hausdorff product theorem is nested inside a task statement and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 38-45",
"status": "verified",
"target_action": "move the unchanged theorem to section level immediately after the activity and retain the direct completion prompt",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C309",
"native": {
"category": "xref_reference",
"evidence": "the replacement xref supplies the needed prior result and removes circular self-citation",
"file": "repo/source/sec_prop_prod_top.ptx",
"id": "O003-C309",
"source_issue": "the proof of lem_Connected_union twice cites the lemma itself for the two-set union result it is using",
"source_locator": "authority lines 83 and 88",
"status": "verified",
"target_action": "cite the earlier foundational activity act_connected_compenent",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C310",
"native": {
"category": "variable_reference",
"evidence": "the corrected symbol is the subspace introduced in the preceding sentence",
"file": "repo/source/sec_prop_prod_top.ptx",
"id": "O003-C310",
"source_issue": "the proof defines X_a but then says the undefined X-prime is connected",
"source_locator": "authority line 122",
"status": "verified",
"target_action": "render X_a as connected",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C311",
"native": {
"category": "map_type",
"evidence": "the formulas and homeomorphism claims are preserved without the incorrect map-type label",
"file": "repo/source/sec_prop_prod_top.ptx",
"id": "O003-C311",
"source_issue": "the factor-identifying homeomorphisms are called inclusion maps although their displayed domains and codomains make them parameterizations into product slices",
"source_locator": "authority lines 120-126",
"status": "verified",
"target_action": "render them neutrally as mappings",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C312",
"native": {
"category": "variable_reference",
"evidence": "the corrected membership refers to the selected member of the finite cover of Y",
"file": "repo/source/sec_prop_prod_top.ptx",
"id": "O003-C312",
"source_issue": "the compactness proof concludes y is in undefined Y_k after defining the finite family V_k",
"source_locator": "authority line 212",
"status": "verified",
"target_action": "render y in V_k",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C313",
"native": {
"category": "grammar_and_logic",
"evidence": "the corrected prose still selects finitely many W_i covering X and then their product strips covering X times Y",
"file": "repo/source/sec_prop_prod_top.ptx",
"id": "O003-C313",
"source_issue": "the final compactness paragraph contains 'the is'; duplicates 'is an open cover of X' after a period; and uses singular agreement for multiple covering sets",
"source_locator": "authority lines 221-229",
"status": "verified",
"target_action": "render a coherent finite-subcover argument with plural agreement",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C314",
"native": {
"category": "definition_reference",
"evidence": "the repaired wording matches the preceding chapter theorem and preserves the definition",
"file": "repo/source/sec_prod_top_summ.ptx",
"id": "O003-C314",
"source_issue": "the subbasis summary calls the collection of all finite intersections 'the set CS' even though CS itself is the subbasis",
"source_locator": "authority line 37",
"status": "verified",
"target_action": "describe the finite-intersection collection as the collection built from CS",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C315",
"native": {
"category": "grammar",
"evidence": "both quantified factors are topological spaces",
"file": "repo/source/sec_prod_top_exer.ptx",
"id": "O003-C315",
"source_issue": "the source says X_1 and X_2 are 'topological space'",
"source_locator": "authority line 87",
"status": "verified",
"target_action": "render the plural 'ruang topologi'",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C316",
"native": {
"category": "punctuation",
"evidence": "the interrogative meaning is explicit without altering the mathematical claim under assessment",
"file": "repo/source/sec_prod_top_exer.ptx",
"id": "O003-C316",
"source_issue": "the compact-factor question ends with a period rather than a question mark",
"source_locator": "authority lines 184-186",
"status": "verified",
"target_action": "render it as a direct question",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C317",
"native": {
"category": "index_chain",
"evidence": "the repaired consecutive-pair condition covers the full displayed sequence through p_m",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C317",
"source_issue": "the k-path sequence begins at p_0 but its adjacency chain begins with p_1 adjacent to p_2 and omits p_0 adjacent to p_1",
"source_locator": "authority lines 46-50",
"status": "verified",
"target_action": "start the adjacency chain with p_0 adjacent to p_1",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C318",
"native": {
"category": "grammar",
"evidence": "both repairs are deterministic typographical normalization",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C318",
"source_issue": "the source says 'we us' and repeats 'if if'",
"source_locator": "authority lines 73 and 75",
"status": "verified",
"target_action": "render the intended verbs and single conditional",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C319",
"native": {
"category": "macro_consistency",
"evidence": "the corrected notation matches the basis definition and all later occurrences",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C319",
"source_issue": "the digital-line activity writes plain Z although every surrounding integer-space reference uses the protected macro backslash-Z",
"source_locator": "authority line 134",
"status": "verified",
"target_action": "render the integer space with backslash-Z",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C320",
"native": {
"category": "definition_consistency",
"evidence": "the repaired recall matches the established definition while preserving the subsequent path-versus-arc distinction",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C320",
"source_issue": "the source recalls a path as a homeomorphism from [0,1] although the book's path definition and the immediately following digital-path definition use the range of a continuous function",
"source_locator": "authority line 172",
"status": "verified",
"target_action": "render a path as the range of a continuous function from [0,1]",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C321",
"native": {
"category": "pretext_structure",
"evidence": "all definition text and index terms remain contiguous with the activity and isolated Chapter 20 schema validation reports zero diagnostics",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C321",
"source_issue": "two formal definitions are nested inside task statements and one additionally places a ul inside a p; both constructions are invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 169-239",
"status": "verified",
"target_action": "move the prerequisite interval prose and both indexed definitions to section level immediately before the same activity; split the invalid list-bearing paragraph into valid definition paragraphs; retain the direct tasks in the activity",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C322",
"native": {
"category": "pretext_structure",
"evidence": "the theorem ID and forward xref are preserved and isolated Chapter 20 schema validation reports zero diagnostics",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C322",
"source_issue": "the theorem thm_digital_Jordan_curve is nested inside an activity task statement and is invalid under the pinned PreTeXt schema",
"source_locator": "authority lines 247-275",
"status": "verified",
"target_action": "move the unchanged theorem to section level immediately after the activity while retaining the task's source citation consequence and direct assessment prompt",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C323",
"native": {
"category": "formula_glyph",
"evidence": "the corrected indices form the stated triples of consecutive points",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C323",
"source_issue": "the theorem contains question-mark glyphs in the subscripts P_{j?1} and P_{i?1} where adjacent indices require subtraction",
"source_locator": "authority lines 293-294",
"status": "verified",
"target_action": "render P_{j-1} and P_{i-1}",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C324",
"native": {
"category": "symbol_case",
"evidence": "the corrected symbols refer to the enumerated points of the digital Jordan curve",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C324",
"source_issue": "the application task switches from the theorem's point labels P_j to undefined lowercase x_j",
"source_locator": "authority line 348",
"status": "verified",
"target_action": "retain the theorem's uppercase P labels throughout",
"unit": "chapter_20_product_topology"
}
},
{
"id": "O003-C325",
"native": {
"category": "grammar",
"evidence": "the correction is grammatical and preserves the neighborhood-intersection definition",
"file": "repo/source/sec_prod_top_app.ptx",
"id": "O003-C325",
"source_issue": "the source says 'let N(x) to be'",
"source_locator": "authority line 316",
"status": "verified",
"target_action": "render the intended definition 'misalkan N(x) adalah'",
"unit": "chapter_20_product_topology"
}
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"id": "O003-T001",
"id_ID": "himpunan",
"note": "Core term",
"status": "approved"
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"id": "O003-T002",
"id_ID": "subhimpunan",
"note": "Himpunan bagian is an accepted introductory alias attested in Indonesian teaching sources; use proper subset only when the source means strict inclusion",
"status": "approved"
}
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"id": "O003-T003",
"native": {
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"id": "O003-T003",
"id_ID": "gabungan",
"note": "Set operation",
"status": "approved"
}
},
{
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"native": {
"en": "intersection",
"id": "O003-T004",
"id_ID": "irisan",
"note": "Set operation",
"status": "approved"
}
},
{
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"native": {
"en": "complement",
"id": "O003-T005",
"id_ID": "komplemen",
"note": "Relative to the stated universal set",
"status": "approved"
}
},
{
"id": "O003-T006",
"native": {
"en": "Cartesian product",
"id": "O003-T006",
"id_ID": "hasil kali Kartesius",
"note": "Capitalize Kartesius",
"status": "approved"
}
},
{
"id": "O003-T007",
"native": {
"en": "interval",
"id": "O003-T007",
"id_ID": "interval",
"note": "Standard Indonesian mathematical loanword",
"status": "approved"
}
},
{
"id": "O003-T008",
"native": {
"en": "open interval",
"id": "O003-T008",
"id_ID": "interval terbuka",
"note": "Do not anticipate topological openness where the source is purely order notation",
"status": "approved"
}
},
{
"id": "O003-T009",
"native": {
"en": "closed interval",
"id": "O003-T009",
"id_ID": "interval tertutup",
"note": "Do not conflate with closed set before introduced",
"status": "approved"
}
},
{
"id": "O003-T010",
"native": {
"en": "topology",
"id": "O003-T010",
"id_ID": "topologi",
"note": "Core term",
"status": "approved"
}
},
{
"id": "O003-T011",
"native": {
"en": "topological space",
"id": "O003-T011",
"id_ID": "ruang topologi",
"note": "Preferred field form in the inspected ITB Universitas Terbuka and UNDIP teaching witnesses; ruang topologis remains intelligible but is not the house term",
"status": "approved"
}
},
{
"id": "O003-T012",
"native": {
"en": "metric space",
"id": "O003-T012",
"id_ID": "ruang metrik",
"note": "Core term",
"status": "approved"
}
},
{
"id": "O003-T013",
"native": {
"en": "neighborhood",
"id": "O003-T013",
"id_ID": "lingkungan",
"note": "Established consistently in the substantive Chapter 7 metric-space unit; do not imply the neighborhood itself must be open",
"status": "approved"
}
},
{
"id": "O003-T014",
"native": {
"en": "closure",
"id": "O003-T014",
"id_ID": "tutupan",
"note": "Topological closure of a set; keep distinct from himpunan tertutup and from ordinary-process penutupan",
"status": "approved"
}
},
{
"id": "O003-T015",
"native": {
"en": "connectedness",
"id": "O003-T015",
"id_ID": "keterhubungan",
"note": "Recheck against later chapter context",
"status": "provisional"
}
},
{
"id": "O003-T016",
"native": {
"en": "function",
"id": "O003-T016",
"id_ID": "fungsi",
"note": "Core Chapter 2 term",
"status": "approved"
}
},
{
"id": "O003-T017",
"native": {
"en": "domain",
"id": "O003-T017",
"id_ID": "domain",
"note": "Use domain consistently; explain daerah asal only if pedagogically useful",
"status": "approved"
}
},
{
"id": "O003-T018",
"native": {
"en": "codomain",
"id": "O003-T018",
"id_ID": "kodomain",
"note": "Keep distinct from range",
"status": "approved"
}
},
{
"id": "O003-T019",
"native": {
"en": "range",
"id": "O003-T019",
"id_ID": "daerah hasil",
"note": "Never collapse into codomain",
"status": "approved"
}
},
{
"id": "O003-T020",
"native": {
"en": "image",
"id": "O003-T020",
"id_ID": "citra",
"note": "For the image of an element or subset under a function; UNDIP Ruang Topologi Fuzzy attests the untranslated variant image but the edition retains the natural Indonesian house term",
"status": "approved"
}
},
{
"id": "O003-T021",
"native": {
"en": "preimage; inverse image",
"id": "O003-T021",
"id_ID": "prapeta",
"note": "Prefer prapeta for a subset under a function and reserve invers for inverse functions; UNDIP Ruang Topologi Fuzzy attests the untranslated variant preimage",
"status": "approved"
}
},
{
"id": "O003-T022",
"native": {
"en": "injection; injective",
"id": "O003-T022",
"id_ID": "injeksi; injektif",
"note": "Use the noun/adjective forms according to grammar",
"status": "approved"
}
},
{
"id": "O003-T023",
"native": {
"en": "surjection; surjective",
"id": "O003-T023",
"id_ID": "surjeksi; surjektif",
"note": "Use the noun/adjective forms according to grammar",
"status": "approved"
}
},
{
"id": "O003-T024",
"native": {
"en": "bijection; bijective",
"id": "O003-T024",
"id_ID": "bijeksi; bijektif",
"note": "Use the noun/adjective forms according to grammar",
"status": "approved"
}
},
{
"id": "O003-T025",
"native": {
"en": "composition; composite",
"id": "O003-T025",
"id_ID": "komposisi; komposit",
"note": "Use komposisi fungsi for the operation",
"status": "approved"
}
},
{
"id": "O003-T026",
"native": {
"en": "inverse function",
"id": "O003-T026",
"id_ID": "fungsi invers",
"note": "Keep distinct from prapeta",
"status": "approved"
}
},
{
"id": "O003-T027",
"native": {
"en": "restriction",
"id": "O003-T027",
"id_ID": "pembatasan",
"note": "Function restricted to a smaller domain",
"status": "approved"
}
},
{
"id": "O003-T028",
"native": {
"en": "extension",
"id": "O003-T028",
"id_ID": "perluasan",
"note": "Function extended to a larger domain",
"status": "approved"
}
},
{
"id": "O003-T029",
"native": {
"en": "identity function",
"id": "O003-T029",
"id_ID": "fungsi identitas",
"note": "Core Chapter 2 term",
"status": "approved"
}
},
{
"id": "O003-T030",
"native": {
"en": "ordered pair",
"id": "O003-T030",
"id_ID": "pasangan terurut",
"note": "Use for graph-of-function pairs",
"status": "approved"
}
},
{
"id": "O003-T031",
"native": {
"en": "invertible",
"id": "O003-T031",
"id_ID": "invertibel",
"note": "Property of a function admitting an inverse function",
"status": "approved"
}
},
{
"id": "O003-T032",
"native": {
"en": "cardinality",
"id": "O003-T032",
"id_ID": "kardinalitas",
"note": "Size of a finite or infinite set",
"status": "approved"
}
},
{
"id": "O003-T033",
"native": {
"en": "finite set",
"id": "O003-T033",
"id_ID": "himpunan berhingga",
"note": "Chapter 2 cardinality term",
"status": "approved"
}
},
{
"id": "O003-T034",
"native": {
"en": "infinite set",
"id": "O003-T034",
"id_ID": "himpunan tak berhingga",
"note": "Chapter 2 cardinality term",
"status": "approved"
}
},
{
"id": "O003-T035",
"native": {
"en": "index set",
"id": "O003-T035",
"id_ID": "himpunan indeks",
"note": "Parameter set for an indexed family",
"status": "approved"
}
},
{
"id": "O003-T036",
"native": {
"en": "indexed family",
"id": "O003-T036",
"id_ID": "keluarga terindeks",
"note": "Prefer explicit diindeks oleh wording in prose",
"status": "approved"
}
},
{
"id": "O003-T037",
"native": {
"en": "element",
"id": "O003-T037",
"id_ID": "unsur",
"note": "Default formal term; the UT Module 1 indexed opening attests elemen as an accepted synonym which may remain in natural cardinality and basis collocations while anggota remains appropriate for membership statements",
"status": "approved"
}
},
{
"id": "O003-T038",
"native": {
"en": "counterexample",
"id": "O003-T038",
"id_ID": "contoh tandingan",
"note": "Avoid contoh penyangkal",
"status": "approved"
}
},
{
"id": "O003-T039",
"native": {
"en": "Euclidean metric",
"id": "O003-T039",
"id_ID": "metrik Euklides",
"note": "Capitalize Euklides",
"status": "approved"
}
},
{
"id": "O003-T040",
"native": {
"en": "taxicab metric",
"id": "O003-T040",
"id_ID": "metrik taksi",
"note": "Use consistently for d_T",
"status": "approved"
}
},
{
"id": "O003-T041",
"native": {
"en": "max metric",
"id": "O003-T041",
"id_ID": "metrik maksimum",
"note": "Use consistently for d_M",
"status": "approved"
}
},
{
"id": "O003-T042",
"native": {
"en": "discrete metric",
"id": "O003-T042",
"id_ID": "metrik diskret",
"note": "Use consistently for the zero-one metric",
"status": "approved"
}
},
{
"id": "O003-T043",
"native": {
"en": "positive definite",
"id": "O003-T043",
"id_ID": "definit positif",
"note": "Metric property",
"status": "approved"
}
},
{
"id": "O003-T044",
"native": {
"en": "symmetric",
"id": "O003-T044",
"id_ID": "simetris",
"note": "Metric property",
"status": "approved"
}
},
{
"id": "O003-T045",
"native": {
"en": "triangle inequality",
"id": "O003-T045",
"id_ID": "pertidaksamaan segitiga",
"note": "Prefer pertidaksamaan over ketaksamaan in this edition",
"status": "approved"
}
},
{
"id": "O003-T046",
"native": {
"en": "open ball",
"id": "O003-T046",
"id_ID": "bola terbuka",
"note": "Bola buka is an attested Indonesian alias; retain the edition's adjective form consistently",
"status": "approved"
}
},
{
"id": "O003-T047",
"native": {
"en": "unit circle",
"id": "O003-T047",
"id_ID": "lingkaran satuan",
"note": "Set of points at distance one from the origin",
"status": "approved"
}
},
{
"id": "O003-T048",
"native": {
"en": "Cauchy-Schwarz inequality",
"id": "O003-T048",
"id_ID": "Pertidaksamaan Cauchy-Schwarz",
"note": "Capitalize in the named result",
"status": "approved"
}
},
{
"id": "O003-T049",
"native": {
"en": "concave",
"id": "O003-T049",
"id_ID": "cekung",
"note": "Real-analysis term used in Chapter 3 exercises",
"status": "approved"
}
},
{
"id": "O003-T050",
"native": {
"en": "graph",
"id": "O003-T050",
"id_ID": "graf",
"note": "Use graph only in protected code or source identifiers",
"status": "approved"
}
},
{
"id": "O003-T051",
"native": {
"en": "vertex",
"id": "O003-T051",
"id_ID": "simpul",
"note": "Graph-theory term",
"status": "approved"
}
},
{
"id": "O003-T052",
"native": {
"en": "edge",
"id": "O003-T052",
"id_ID": "sisi",
"note": "Graph-theory term",
"status": "approved"
}
},
{
"id": "O003-T053",
"native": {
"en": "shortest path",
"id": "O003-T053",
"id_ID": "lintasan terpendek",
"note": "Weighted-graph metric term",
"status": "approved"
}
},
{
"id": "O003-T054",
"native": {
"en": "Hamming metric",
"id": "O003-T054",
"id_ID": "metrik Hamming",
"note": "Named coding-theory metric",
"status": "approved"
}
},
{
"id": "O003-T055",
"native": {
"en": "Hamming distance",
"id": "O003-T055",
"id_ID": "jarak Hamming",
"note": "Distance value induced by the Hamming metric",
"status": "approved"
}
},
{
"id": "O003-T056",
"native": {
"en": "binary system",
"id": "O003-T056",
"id_ID": "sistem biner",
"note": "Digital-coding term",
"status": "approved"
}
},
{
"id": "O003-T057",
"native": {
"en": "word (coding theory)",
"id": "O003-T057",
"id_ID": "kata",
"note": "An element of X^n in the coding-theory context",
"status": "approved"
}
},
{
"id": "O003-T058",
"native": {
"en": "code",
"id": "O003-T058",
"id_ID": "kode",
"note": "A designated subset of words",
"status": "approved"
}
},
{
"id": "O003-T059",
"native": {
"en": "code word",
"id": "O003-T059",
"id_ID": "kata kode",
"note": "An admissible word belonging to a code",
"status": "approved"
}
},
{
"id": "O003-T060",
"native": {
"en": "encoding",
"id": "O003-T060",
"id_ID": "pengodean",
"note": "Digital-message operation",
"status": "approved"
}
},
{
"id": "O003-T061",
"native": {
"en": "decoding",
"id": "O003-T061",
"id_ID": "pendekodean",
"note": "Recovery of a message from its encoded or received form",
"status": "approved"
}
},
{
"id": "O003-T062",
"native": {
"en": "error",
"id": "O003-T062",
"id_ID": "galat",
"note": "Use for transmission and mathematical errors; retain salah only for ordinary misspelling",
"status": "approved"
}
},
{
"id": "O003-T063",
"native": {
"en": "string",
"id": "O003-T063",
"id_ID": "untai",
"note": "Computer-science and finite-alphabet term; introduce context explicitly",
"status": "approved"
}
},
{
"id": "O003-T064",
"native": {
"en": "alphabet",
"id": "O003-T064",
"id_ID": "alfabet",
"note": "Fixed set of allowable symbols",
"status": "approved"
}
},
{
"id": "O003-T065",
"native": {
"en": "deletion",
"id": "O003-T065",
"id_ID": "penghapusan",
"note": "Levenshtein edit operation",
"status": "approved"
}
},
{
"id": "O003-T066",
"native": {
"en": "insertion",
"id": "O003-T066",
"id_ID": "penyisipan",
"note": "Levenshtein edit operation",
"status": "approved"
}
},
{
"id": "O003-T067",
"native": {
"en": "substitution",
"id": "O003-T067",
"id_ID": "substitusi",
"note": "Levenshtein edit operation",
"status": "approved"
}
},
{
"id": "O003-T068",
"native": {
"en": "Levenshtein metric",
"id": "O003-T068",
"id_ID": "metrik Levenshtein",
"note": "Named edit-distance metric",
"status": "approved"
}
},
{
"id": "O003-T069",
"native": {
"en": "Levenshtein distance",
"id": "O003-T069",
"id_ID": "jarak Levenshtein",
"note": "Minimum number of permitted edits",
"status": "approved"
}
},
{
"id": "O003-T070",
"native": {
"en": "spell checker",
"id": "O003-T070",
"id_ID": "pemeriksa ejaan",
"note": "Application of edit distance",
"status": "approved"
}
},
{
"id": "O003-T071",
"native": {
"en": "speech recognition",
"id": "O003-T071",
"id_ID": "pengenalan wicara",
"note": "Application of edit distance",
"status": "approved"
}
},
{
"id": "O003-T072",
"native": {
"en": "DNA strand",
"id": "O003-T072",
"id_ID": "untai DNA",
"note": "Biological string-model term",
"status": "approved"
}
},
{
"id": "O003-T073",
"native": {
"en": "lower bound",
"id": "O003-T073",
"id_ID": "batas bawah",
"note": "Order-theoretic term for subsets of the reals",
"status": "approved"
}
},
{
"id": "O003-T074",
"native": {
"en": "bounded below",
"id": "O003-T074",
"id_ID": "terbatas di bawah",
"note": "Property of a set having a lower bound",
"status": "approved"
}
},
{
"id": "O003-T075",
"native": {
"en": "greatest lower bound",
"id": "O003-T075",
"id_ID": "batas bawah terbesar",
"note": "Use alongside infimum at first introduction",
"status": "approved"
}
},
{
"id": "O003-T076",
"native": {
"en": "infimum",
"id": "O003-T076",
"id_ID": "infimum",
"note": "Standard Indonesian mathematical loanword",
"status": "approved"
}
},
{
"id": "O003-T077",
"native": {
"en": "upper bound",
"id": "O003-T077",
"id_ID": "batas atas",
"note": "Order-theoretic dual of lower bound",
"status": "approved"
}
},
{
"id": "O003-T078",
"native": {
"en": "bounded above",
"id": "O003-T078",
"id_ID": "terbatas di atas",
"note": "Property of a set having an upper bound",
"status": "approved"
}
},
{
"id": "O003-T079",
"native": {
"en": "least upper bound",
"id": "O003-T079",
"id_ID": "batas atas terkecil",
"note": "Use alongside supremum at first introduction",
"status": "approved"
}
},
{
"id": "O003-T080",
"native": {
"en": "supremum",
"id": "O003-T080",
"id_ID": "supremum",
"note": "Standard Indonesian mathematical loanword",
"status": "approved"
}
},
{
"id": "O003-T081",
"native": {
"en": "completeness axiom",
"id": "O003-T081",
"id_ID": "aksioma kelengkapan",
"note": "Completeness property of the real number system",
"status": "approved"
}
},
{
"id": "O003-T082",
"native": {
"en": "distance from a point to a set",
"id": "O003-T082",
"id_ID": "jarak dari titik ke himpunan",
"note": "Point-to-set distance defined by an infimum",
"status": "approved"
}
},
{
"id": "O003-T083",
"native": {
"en": "bounded",
"id": "O003-T083",
"id_ID": "terbatas",
"note": "For a real subset bounded above and below",
"status": "approved"
}
},
{
"id": "O003-T084",
"native": {
"en": "dense",
"id": "O003-T084",
"id_ID": "rapat",
"note": "Topological density term",
"status": "approved"
}
},
{
"id": "O003-T085",
"native": {
"en": "Archimedean property",
"id": "O003-T085",
"id_ID": "sifat Archimedes",
"note": "Standard Indonesian name for the real-number property",
"status": "approved"
}
},
{
"id": "O003-T086",
"native": {
"en": "Well-Ordering Principle",
"id": "O003-T086",
"id_ID": "Prinsip Pengurutan Baik",
"note": "Capitalize as the named principle",
"status": "approved"
}
},
{
"id": "O003-T087",
"native": {
"en": "supremum metric",
"id": "O003-T087",
"id_ID": "metrik supremum",
"note": "Metric on continuous functions over a compact interval",
"status": "approved"
}
},
{
"id": "O003-T088",
"native": {
"en": "uniform metric",
"id": "O003-T088",
"id_ID": "metrik seragam",
"note": "Alternative name for the supremum metric",
"status": "approved"
}
},
{
"id": "O003-T089",
"native": {
"en": "rational number",
"id": "O003-T089",
"id_ID": "bilangan rasional",
"note": "Number-system term",
"status": "approved"
}
},
{
"id": "O003-T090",
"native": {
"en": "irrational number",
"id": "O003-T090",
"id_ID": "bilangan irasional",
"note": "Number-system term",
"status": "approved"
}
},
{
"id": "O003-T091",
"native": {
"en": "natural number",
"id": "O003-T091",
"id_ID": "bilangan asli",
"note": "Positive integers in the source convention",
"status": "approved"
}
},
{
"id": "O003-T092",
"native": {
"en": "positive integer",
"id": "O003-T092",
"id_ID": "bilangan bulat positif",
"note": "Explicitly distinguishes from nonnegative integers",
"status": "approved"
}
},
{
"id": "O003-T093",
"native": {
"en": "continuous function",
"id": "O003-T093",
"id_ID": "fungsi kontinu",
"note": "Standard Indonesian mathematical term also attested in both inspected UNDIP topology catalog witnesses",
"status": "approved"
}
},
{
"id": "O003-T094",
"native": {
"en": "continuity",
"id": "O003-T094",
"id_ID": "kekontinuan",
"note": "Property of being continuous; kontinuitas is attested but is not the edition's nominal house term",
"status": "approved"
}
},
{
"id": "O003-T095",
"native": {
"en": "continuous at a point",
"id": "O003-T095",
"id_ID": "kontinu di suatu titik",
"note": "Use in epsilon-delta definitions",
"status": "approved"
}
},
{
"id": "O003-T096",
"native": {
"en": "epsilon-delta definition",
"id": "O003-T096",
"id_ID": "definisi epsilon-delta",
"note": "Use ASCII names in prose and preserve Greek symbols in mathematics",
"status": "approved"
}
},
{
"id": "O003-T097",
"native": {
"en": "Intermediate Value Theorem",
"id": "O003-T097",
"id_ID": "Teorema Nilai Antara",
"note": "Capitalize as the named theorem",
"status": "approved"
}
},
{
"id": "O003-T098",
"native": {
"en": "open set",
"id": "O003-T098",
"id_ID": "himpunan terbuka",
"note": "Himpunan buka is an attested Indonesian alias; retain the edition's adjective form consistently",
"status": "approved"
}
},
{
"id": "O003-T099",
"native": {
"en": "radius",
"id": "O003-T099",
"id_ID": "jari-jari",
"note": "Open-ball radius",
"status": "approved"
}
},
{
"id": "O003-T100",
"native": {
"en": "centered at",
"id": "O003-T100",
"id_ID": "berpusat di",
"note": "Use for balls and metric diagrams",
"status": "approved"
}
},
{
"id": "O003-T101",
"native": {
"en": "weighted graph",
"id": "O003-T101",
"id_ID": "graf berbobot",
"note": "Finite graph carrying positive edge weights",
"status": "approved"
}
},
{
"id": "O003-T102",
"native": {
"en": "indexing set",
"id": "O003-T102",
"id_ID": "himpunan indeks",
"note": "Index family terminology",
"status": "approved"
}
},
{
"id": "O003-T103",
"native": {
"en": "open map",
"id": "O003-T103",
"id_ID": "pemetaan terbuka",
"note": "Map that sends every open set to an open set",
"status": "approved"
}
},
{
"id": "O003-T104",
"native": {
"en": "interior; interior of a set",
"id": "O003-T104",
"id_ID": "interior; interior suatu himpunan",
"note": "Set of all interior points; keep distinct from closure",
"status": "approved"
}
},
{
"id": "O003-T105",
"native": {
"en": "interior point",
"id": "O003-T105",
"id_ID": "titik interior",
"note": "A point for which the containing set is a neighborhood",
"status": "approved"
}
},
{
"id": "O003-T106",
"native": {
"en": "affine function; affine map",
"id": "O003-T106",
"id_ID": "fungsi afin; pemetaan afin",
"note": "Use for x maps to ax plus b when b is arbitrary; reserve fungsi linear for b equal to zero over the reals",
"status": "approved"
}
},
{
"id": "O003-T107",
"native": {
"en": "basis for open sets",
"id": "O003-T107",
"id_ID": "basis",
"note": "Family of open balls or other generators whose unions give the open sets",
"status": "approved"
}
},
{
"id": "O003-T108",
"native": {
"en": "arbitrary union",
"id": "O003-T108",
"id_ID": "gabungan sebarang",
"note": "Topology closure property with no finiteness restriction on the indexed family",
"status": "approved"
}
},
{
"id": "O003-T109",
"native": {
"en": "arbitrary intersection",
"id": "O003-T109",
"id_ID": "irisan sebarang",
"note": "Need not preserve openness",
"status": "approved"
}
},
{
"id": "O003-T110",
"native": {
"en": "finite intersection",
"id": "O003-T110",
"id_ID": "irisan berhingga",
"note": "Preserves openness",
"status": "approved"
}
},
{
"id": "O003-T111",
"native": {
"en": "biconditional statement",
"id": "O003-T111",
"id_ID": "pernyataan bikondisional",
"note": "Statement whose forward and reverse implications must both be proved",
"status": "approved"
}
},
{
"id": "O003-T112",
"native": {
"en": "reverse containment; reverse inclusion",
"id": "O003-T112",
"id_ID": "inklusi sebaliknya",
"note": "Proof terminology for the opposite set inclusion",
"status": "approved"
}
},
{
"id": "O003-T113",
"native": {
"en": "sequence",
"id": "O003-T113",
"id_ID": "barisan",
"note": "Use for functions from the positive integers into a space",
"status": "approved"
}
},
{
"id": "O003-T114",
"native": {
"en": "term of a sequence",
"id": "O003-T114",
"id_ID": "suku barisan",
"note": "Individual value indexed by n",
"status": "approved"
}
},
{
"id": "O003-T115",
"native": {
"en": "converges to",
"id": "O003-T115",
"id_ID": "konvergen ke",
"note": "Relational wording for a sequence and its limit",
"status": "approved"
}
},
{
"id": "O003-T116",
"native": {
"en": "divergent",
"id": "O003-T116",
"id_ID": "divergen",
"note": "Use when a sequence has no limit in the stated metric space",
"status": "approved"
}
},
{
"id": "O003-T117",
"native": {
"en": "pointwise convergence",
"id": "O003-T117",
"id_ID": "konvergensi titik demi titik",
"note": "Function-sequence convergence evaluated separately at each input; konvergen per titik is an attested relational alias",
"status": "approved"
}
},
{
"id": "O003-T118",
"native": {
"en": "eventually constant",
"id": "O003-T118",
"id_ID": "pada akhirnya konstan",
"note": "All terms equal one fixed value beyond some index",
"status": "approved"
}
},
{
"id": "O003-T119",
"native": {
"en": "ambient space",
"id": "O003-T119",
"id_ID": "ruang ambien",
"note": "Larger space used to distinguish ambient convergence from convergence inside a subspace",
"status": "approved"
}
},
{
"id": "O003-T120",
"native": {
"en": "bounded sequence",
"id": "O003-T120",
"id_ID": "barisan terbatas",
"note": "A sequence whose range is a bounded subset",
"status": "approved"
}
},
{
"id": "O003-T121",
"native": {
"en": "limit of a sequence",
"id": "O003-T121",
"id_ID": "limit barisan",
"note": "Use consistently rather than batas barisan",
"status": "approved"
}
},
{
"id": "O003-T122",
"native": {
"en": "convergence",
"id": "O003-T122",
"id_ID": "konvergensi",
"note": "Kekonvergenan is an attested Indonesian alias; retain konvergensi as the edition's concise nominal house term",
"status": "approved"
}
},
{
"id": "O003-T123",
"native": {
"en": "closed set",
"id": "O003-T123",
"id_ID": "himpunan tertutup",
"note": "Keep distinct from tutupan of a set",
"status": "approved"
}
},
{
"id": "O003-T124",
"native": {
"en": "compactness",
"id": "O003-T124",
"id_ID": "kekompakan",
"note": "Property corresponding to a compact space",
"status": "approved"
}
},
{
"id": "O003-T125",
"native": {
"en": "compact space",
"id": "O003-T125",
"id_ID": "ruang kompak",
"note": "Attested in the Universitas Terbuka topology overview",
"status": "approved"
}
},
{
"id": "O003-T126",
"native": {
"en": "product topology",
"id": "O003-T126",
"id_ID": "topologi hasil kali",
"note": "Attested in the inspected ITB teaching witness",
"status": "approved"
}
},
{
"id": "O003-T127",
"native": {
"en": "uniform topology",
"id": "O003-T127",
"id_ID": "topologi seragam",
"note": "Use when the topology is induced by a uniform metric or uniform structure",
"status": "approved"
}
},
{
"id": "O003-T128",
"native": {
"en": "subbasis",
"id": "O003-T128",
"id_ID": "subbasis",
"note": "Standard Indonesian mathematical loanword",
"status": "approved"
}
},
{
"id": "O003-T129",
"native": {
"en": "boundary point",
"id": "O003-T129",
"id_ID": "titik batas",
"note": "Attested in official Indonesian university mathematics curricula; keep distinct from limit barisan",
"status": "approved"
}
},
{
"id": "O003-T130",
"native": {
"en": "limit point; accumulation point",
"id": "O003-T130",
"id_ID": "titik limit (sinonim: titik akumulasi)",
"note": "The GVSU metric-space chapter explicitly uses the two source terms synonymously; titik limit is the attested canonical form and titik akumulasi is retained only where the source itself presents the synonym pair",
"status": "approved"
}
},
{
"id": "O003-T131",
"native": {
"en": "isolated point",
"id": "O003-T131",
"id_ID": "titik terasing",
"note": "Attested alongside titik limit and titik batas in the official UGM mathematics curriculum",
"status": "approved"
}
},
{
"id": "O003-T132",
"native": {
"en": "boundary of a set",
"id": "O003-T132",
"id_ID": "batas suatu himpunan",
"note": "The set of all boundary points; keep distinct from limit barisan and topological tutupan",
"status": "approved"
}
},
{
"id": "O003-T133",
"native": {
"en": "subspace; metric subspace",
"id": "O003-T133",
"id_ID": "subruang; subruang metrik",
"note": "Use subruang dari ruang metrik when the ambient space must be explicit",
"status": "approved"
}
},
{
"id": "O003-T134",
"native": {
"en": "product metric space",
"id": "O003-T134",
"id_ID": "ruang metrik hasil kali",
"note": "Align with hasil kali Kartesius and topologi hasil kali; avoid the unnecessary loanword produk",
"status": "approved"
}
},
{
"id": "O003-T135",
"native": {
"en": "product metric",
"id": "O003-T135",
"id_ID": "metrik hasil kali",
"note": "Keep distinct from topologi hasil kali",
"status": "approved"
}
},
{
"id": "O003-T136",
"native": {
"en": "coordinate space",
"id": "O003-T136",
"id_ID": "ruang koordinat",
"note": "A factor in a finite metric product",
"status": "approved"
}
},
{
"id": "O003-T137",
"native": {
"en": "factor space",
"id": "O003-T137",
"id_ID": "ruang faktor",
"note": "Use only in the product context here; do not use it for a quotient space",
"status": "approved"
}
},
{
"id": "O003-T138",
"native": {
"en": "Hilbert space",
"id": "O003-T138",
"id_ID": "ruang Hilbert",
"note": "Standard named-space form",
"status": "approved"
}
},
{
"id": "O003-T139",
"native": {
"en": "norm",
"id": "O003-T139",
"id_ID": "norma",
"note": "The square-sum norm on the displayed sequence space",
"status": "approved"
}
},
{
"id": "O003-T140",
"native": {
"en": "non-decreasing sequence",
"id": "O003-T140",
"id_ID": "barisan tak menurun",
"note": "Equality is allowed; do not strengthen to a strictly increasing sequence",
"status": "approved"
}
},
{
"id": "O003-T141",
"native": {
"en": "embedding; embedded",
"id": "O003-T141",
"id_ID": "pembenaman; tertanam",
"note": "In prose use ditanamkan sebagai subruang",
"status": "approved"
}
},
{
"id": "O003-T142",
"native": {
"en": "basis for a topology",
"id": "O003-T142",
"id_ID": "basis untuk topologi",
"note": "Use basis as the established Indonesian mathematical term; specify untuk topologi at first definition",
"status": "approved"
}
},
{
"id": "O003-T143",
"native": {
"en": "open set",
"id": "O003-T143",
"id_ID": "himpunan terbuka",
"note": "Core topology term; do not shorten to terbuka when the noun is needed",
"status": "approved"
}
},
{
"id": "O003-T144",
"native": {
"en": "indiscrete topology",
"id": "O003-T144",
"id_ID": "topologi indiskret",
"note": "Preferred Indonesian rendering alongside topologi diskret",
"status": "approved"
}
},
{
"id": "O003-T145",
"native": {
"en": "finite complement topology; cofinite topology",
"id": "O003-T145",
"id_ID": "topologi komplemen berhingga; topologi kofinit",
"note": "Use topologi komplemen berhingga in exposition and retain kofinit as the standard synonym",
"status": "approved"
}
},
{
"id": "O003-T146",
"native": {
"en": "metrizable",
"id": "O003-T146",
"id_ID": "termetriskan",
"note": "Use for a topological space realizable by a metric",
"status": "approved"
}
},
{
"id": "O003-T147",
"native": {
"en": "Golomb space",
"id": "O003-T147",
"id_ID": "ruang Golomb",
"note": "Named space; retain Golomb unchanged",
"status": "approved"
}
},
{
"id": "O003-T148",
"native": {
"en": "coarser topology; weaker topology",
"id": "O003-T148",
"id_ID": "topologi lebih kasar; topologi lebih lemah",
"note": "Order terminology for inclusion of topologies",
"status": "approved"
}
},
{
"id": "O003-T149",
"native": {
"en": "finer topology; stronger topology",
"id": "O003-T149",
"id_ID": "topologi lebih halus; topologi lebih kuat",
"note": "Order terminology dual to coarser/weaker",
"status": "approved"
}
},
{
"id": "O003-T150",
"native": {
"en": "digital line topology",
"id": "O003-T150",
"id_ID": "topologi garis digital",
"note": "Use garis digital for the associated one-dimensional pixel model",
"status": "approved"
}
},
{
"id": "O003-T151",
"native": {
"en": "particular point topology",
"id": "O003-T151",
"id_ID": "topologi titik tertentu",
"note": "Standard descriptive Indonesian rendering",
"status": "approved"
}
},
{
"id": "O003-T152",
"native": {
"en": "excluded point topology",
"id": "O003-T152",
"id_ID": "topologi titik yang dikecualikan",
"note": "Keep distinct from particular point topology",
"status": "approved"
}
},
{
"id": "O003-T153",
"native": {
"en": "Zariski topology",
"id": "O003-T153",
"id_ID": "topologi Zariski",
"note": "Named topology; retain Zariski unchanged",
"status": "approved"
}
},
{
"id": "O003-T154",
"native": {
"en": "closed set in a topological space",
"id": "O003-T154",
"id_ID": "himpunan tertutup dalam ruang topologi",
"note": "Extends the established metric-space term without implying metrizability",
"status": "approved"
}
},
{
"id": "O003-T155",
"native": {
"en": "Hausdorff space",
"id": "O003-T155",
"id_ID": "ruang Hausdorff",
"note": "Standard proper-name form; retain Hausdorff unchanged",
"status": "approved"
}
},
{
"id": "O003-T156",
"native": {
"en": "separation axiom",
"id": "O003-T156",
"id_ID": "aksioma separasi",
"note": "Official Indonesian topology teaching and journal sources use aksioma separasi; use with unchanged symbols T_1 through T_4",
"status": "approved"
}
},
{
"id": "O003-T157",
"native": {
"en": "trivial topology",
"id": "O003-T157",
"id_ID": "topologi trivial",
"note": "Retain as the explicit synonym paired with topologi indiskret",
"status": "approved"
}
},
{
"id": "O003-T158",
"native": {
"en": "singleton set",
"id": "O003-T158",
"id_ID": "himpunan beranggota tunggal",
"note": "Use the natural descriptive Indonesian form in reader prose",
"status": "approved"
}
},
{
"id": "O003-T159",
"native": {
"en": "clopen set",
"id": "O003-T159",
"id_ID": "himpunan buka-tutup",
"note": "Introduce the transparent Indonesian form and retain clopen once as the source's closed-open portmanteau",
"status": "approved"
}
},
{
"id": "O003-T160",
"native": {
"en": "derived set",
"id": "O003-T160",
"id_ID": "himpunan turunan",
"note": "Use for the set A' of all limit points of A; keep distinct from closure",
"status": "approved"
}
},
{
"id": "O003-T161",
"native": {
"en": "regular space",
"id": "O003-T161",
"id_ID": "ruang reguler",
"note": "Official UGM topology curriculum uses ruang reguler; record regular as an encountered spelling variant only",
"status": "approved"
}
},
{
"id": "O003-T162",
"native": {
"en": "normal space",
"id": "O003-T162",
"id_ID": "ruang normal",
"note": "Official Indonesian topology teaching and journal sources use ruang normal",
"status": "approved"
}
},
{
"id": "O003-T163",
"native": {
"en": "Fréchet space",
"id": "O003-T163",
"id_ID": "ruang Fréchet",
"note": "Retain the proper name and diacritic in reader prose and index terms",
"status": "approved"
}
},
{
"id": "O003-T164",
"native": {
"en": "K-topology",
"id": "O003-T164",
"id_ID": "topologi K",
"note": "Use Indonesian head-first order and retain the mathematical symbol K",
"status": "approved"
}
},
{
"id": "O003-T165",
"native": {
"en": "Niemytzki plane",
"id": "O003-T165",
"id_ID": "bidang Niemytzki",
"note": "Retain the proper name and translate the geometric noun",
"status": "approved"
}
},
{
"id": "O003-T166",
"native": {
"en": "Double Origin topology",
"id": "O003-T166",
"id_ID": "topologi Titik Asal Ganda",
"note": "Use a transparent Indonesian name while preserving the two distinguished origins in the definition",
"status": "approved"
}
},
{
"id": "O003-T167",
"native": {
"en": "homeomorphism",
"id": "O003-T167",
"id_ID": "homeomorfisme",
"note": "Standard Indonesian mathematical loanword for a bicontinuous bijection; UNDIP Ruang Topologi Fuzzy attests homeomorphisma as a variant but does not justify corpus-wide replacement",
"status": "approved"
}
},
{
"id": "O003-T168",
"native": {
"en": "homeomorphic",
"id": "O003-T168",
"id_ID": "homeomorfik",
"note": "Adjectival form paired consistently with homeomorfisme",
"status": "approved"
}
},
{
"id": "O003-T169",
"native": {
"en": "metric equivalence",
"id": "O003-T169",
"id_ID": "ekuivalensi metrik",
"note": "Use for equivalence induced by an isometry and keep distinct from topological equivalence",
"status": "approved"
}
},
{
"id": "O003-T170",
"native": {
"en": "topological equivalence",
"id": "O003-T170",
"id_ID": "ekuivalensi topologis",
"note": "Use for equivalence induced by a homeomorphism",
"status": "approved"
}
},
{
"id": "O003-T171",
"native": {
"en": "topological invariant",
"id": "O003-T171",
"id_ID": "invarian topologis",
"note": "Property preserved under homeomorphism",
"status": "approved"
}
},
{
"id": "O003-T172",
"native": {
"en": "open map; open function",
"id": "O003-T172",
"id_ID": "pemetaan terbuka",
"note": "Use pemetaan as the natural mathematical noun while retaining the source's function concept",
"status": "approved"
}
},
{
"id": "O003-T173",
"native": {
"en": "closed map; closed function",
"id": "O003-T173",
"id_ID": "pemetaan tertutup",
"note": "Parallel term to pemetaan terbuka",
"status": "approved"
}
},
{
"id": "O003-T174",
"native": {
"en": "metrically equivalent",
"id": "O003-T174",
"id_ID": "ekuivalen secara metrik",
"note": "Adjectival form paired with ekuivalensi metrik",
"status": "approved"
}
},
{
"id": "O003-T175",
"native": {
"en": "isometry",
"id": "O003-T175",
"id_ID": "isometri",
"note": "Standard Indonesian mathematical loanword for the book's bijective distance-preserving map convention",
"status": "approved"
}
},
{
"id": "O003-T176",
"native": {
"en": "topologically equivalent",
"id": "O003-T176",
"id_ID": "ekuivalen secara topologis",
"note": "Adjectival form paired with ekuivalensi topologis",
"status": "approved"
}
},
{
"id": "O003-T177",
"native": {
"en": "identity mapping",
"id": "O003-T177",
"id_ID": "pemetaan identitas",
"note": "Standard term for the map sending every point to itself",
"status": "approved"
}
},
{
"id": "O003-T178",
"native": {
"en": "underlying set",
"id": "O003-T178",
"id_ID": "himpunan dasar",
"note": "Use for the common carrier set beneath one or more structures",
"status": "approved"
}
},
{
"id": "O003-T179",
"native": {
"en": "deformation",
"id": "O003-T179",
"id_ID": "deformasi",
"note": "Use only in the informal topological sense and do not imply differentiable smoothness",
"status": "approved"
}
},
{
"id": "O003-T180",
"native": {
"en": "relation",
"id": "O003-T180",
"id_ID": "relasi",
"note": "Standard Indonesian term for a subset of a Cartesian square",
"status": "approved"
}
},
{
"id": "O003-T181",
"native": {
"en": "related to",
"id": "O003-T181",
"id_ID": "berelasi dengan",
"note": "Use for the notation a ~ b and distinguish it from equality",
"status": "approved"
}
},
{
"id": "O003-T182",
"native": {
"en": "reflexive",
"id": "O003-T182",
"id_ID": "refleksif",
"note": "Standard property of a relation",
"status": "approved"
}
},
{
"id": "O003-T183",
"native": {
"en": "symmetric",
"id": "O003-T183",
"id_ID": "simetris",
"note": "Standard property of a relation",
"status": "approved"
}
},
{
"id": "O003-T184",
"native": {
"en": "transitive",
"id": "O003-T184",
"id_ID": "transitif",
"note": "Standard property of a relation",
"status": "approved"
}
},
{
"id": "O003-T185",
"native": {
"en": "equivalence relation",
"id": "O003-T185",
"id_ID": "relasi ekuivalensi",
"note": "Stable term for reflexive symmetric transitive relation",
"status": "approved"
}
},
{
"id": "O003-T186",
"native": {
"en": "equivalence class",
"id": "O003-T186",
"id_ID": "kelas ekuivalensi",
"note": "Use for the blocks in the partition induced by an equivalence relation",
"status": "approved"
}
},
{
"id": "O003-T187",
"native": {
"en": "disjoint union",
"id": "O003-T187",
"id_ID": "gabungan saling lepas",
"note": "Use for a union of pairwise disjoint subsets",
"status": "approved"
}
},
{
"id": "O003-T188",
"native": {
"en": "equals relation",
"id": "O003-T188",
"id_ID": "relasi kesamaan",
"note": "Use for the equality relation on the integers example",
"status": "approved"
}
},
{
"id": "O003-T189",
"native": {
"en": "homeomorphism class",
"id": "O003-T189",
"id_ID": "kelas homeomorfisme",
"note": "Use for equivalence classes under homeomorphism",
"status": "approved"
}
},
{
"id": "O003-T190",
"native": {
"en": "topological invariant",
"id": "O003-T190",
"id_ID": "invarian topologis",
"note": "Stable noun for a property preserved by homeomorphism",
"status": "approved"
}
},
{
"id": "O003-T191",
"native": {
"en": "topological property",
"id": "O003-T191",
"id_ID": "sifat topologis",
"note": "Parallel reader term for an invariant property",
"status": "approved"
}
},
{
"id": "O003-T192",
"native": {
"en": "indiscrete topology",
"id": "O003-T192",
"id_ID": "topologi indiskret",
"note": "Standard Indonesian topology term",
"status": "approved"
}
},
{
"id": "O003-T193",
"native": {
"en": "discrete topology",
"id": "O003-T193",
"id_ID": "topologi diskret",
"note": "Standard Indonesian topology term",
"status": "approved"
}
},
{
"id": "O003-T194",
"native": {
"en": "finite complement topology",
"id": "O003-T194",
"id_ID": "topologi komplemen berhingga",
"note": "Normalized to the earlier controlling O003-T145 term; topologi kofinit remains an accepted synonym",
"status": "approved"
}
},
{
"id": "O003-T195",
"native": {
"en": "subspace",
"id": "O003-T195",
"id_ID": "subruang",
"note": "Standard Indonesian topology term; preserve the source convention that a subspace is nonempty",
"status": "approved"
}
},
{
"id": "O003-T196",
"native": {
"en": "subspace topology",
"id": "O003-T196",
"id_ID": "topologi subruang",
"note": "Topology inherited by a subset from the ambient topological space",
"status": "approved"
}
},
{
"id": "O003-T197",
"native": {
"en": "relatively open",
"id": "O003-T197",
"id_ID": "terbuka relatif",
"note": "On first use state the ambient subset explicitly as terbuka relatif terhadap A",
"status": "approved"
}
},
{
"id": "O003-T198",
"native": {
"en": "relatively closed",
"id": "O003-T198",
"id_ID": "tertutup relatif",
"note": "On first use state the ambient subset explicitly as tertutup relatif terhadap A",
"status": "approved"
}
},
{
"id": "O003-T199",
"native": {
"en": "relative topology",
"id": "O003-T199",
"id_ID": "topologi relatif",
"note": "Synonym for topologi subruang when the source uses relative topology; directly attested in the UNDIP Ruang Topologi Fuzzy synopsis",
"status": "approved"
}
},
{
"id": "O003-T200",
"native": {
"en": "induced topology",
"id": "O003-T200",
"id_ID": "topologi terinduksi",
"note": "Use when the source emphasizes that the ambient topology induces the subspace topology",
"status": "approved"
}
},
{
"id": "O003-T201",
"native": {
"en": "basis for a subspace",
"id": "O003-T201",
"id_ID": "basis untuk subruang",
"note": "Preserve basis macro and intersection formulas",
"status": "approved"
}
},
{
"id": "O003-T202",
"native": {
"en": "restriction of a metric or function",
"id": "O003-T202",
"id_ID": "pembatasan metrik atau fungsi",
"note": "Use pembatasan for a map or metric restricted to a subset",
"status": "approved"
}
},
{
"id": "O003-T203",
"native": {
"en": "nonempty subset",
"id": "O003-T203",
"id_ID": "subhimpunan tak kosong",
"note": "Stable formulation for the upstream chapter's explicit nonempty-subspace convention",
"status": "approved"
}
},
{
"id": "O003-T204",
"native": {
"en": "quotient space",
"id": "O003-T204",
"id_ID": "ruang kuosien",
"note": "Standard topology term; do not conflate with ruang faktor in the product-space context",
"status": "approved"
}
},
{
"id": "O003-T205",
"native": {
"en": "quotient",
"id": "O003-T205",
"id_ID": "kuosien atau hasil bagi",
"note": "Use hasil bagi for elementary arithmetic and kuosien for the topological construction",
"status": "approved"
}
},
{
"id": "O003-T206",
"native": {
"en": "congruence modulo n",
"id": "O003-T206",
"id_ID": "kongruensi modulo n",
"note": "Standard number-theoretic formulation; modulo corrects the upstream typo module",
"status": "approved"
}
},
{
"id": "O003-T207",
"native": {
"en": "identify points",
"id": "O003-T207",
"id_ID": "mengidentifikasi titik",
"note": "Use for declaring points equivalent in a quotient construction",
"status": "approved"
}
},
{
"id": "O003-T208",
"native": {
"en": "glue points or edges",
"id": "O003-T208",
"id_ID": "merekatkan titik atau sisi",
"note": "Geometric reader term for quotient identification",
"status": "approved"
}
},
{
"id": "O003-T209",
"native": {
"en": "quotient topology",
"id": "O003-T209",
"id_ID": "topologi kuosien",
"note": "Topology placed on the quotient codomain by the inverse-image criterion",
"status": "approved"
}
},
{
"id": "O003-T210",
"native": {
"en": "collapse or collapsing",
"id": "O003-T210",
"id_ID": "penciutan atau menciutkan",
"note": "Use the noun or verb according to grammar when quotient identification contracts a subspace",
"status": "approved"
}
},
{
"id": "O003-T211",
"native": {
"en": "quotient map",
"id": "O003-T211",
"id_ID": "pemetaan kuosien",
"note": "Surjective map characterized by openness of inverse images; use pemetaan consistently with open and closed maps",
"status": "approved"
}
},
{
"id": "O003-T212",
"native": {
"en": "identification space",
"id": "O003-T212",
"id_ID": "ruang identifikasi",
"note": "Synonym emphasizing the equivalence-class construction of a quotient space",
"status": "approved"
}
},
{
"id": "O003-T213",
"native": {
"en": "floor function",
"id": "O003-T213",
"id_ID": "fungsi lantai",
"note": "Standard term for the greatest-integer function represented by floor brackets",
"status": "approved"
}
},
{
"id": "O003-T214",
"native": {
"en": "Möbius strip",
"id": "O003-T214",
"id_ID": "pita Möbius",
"note": "Standard Indonesian name; retain the proper name with diaeresis",
"status": "approved"
}
},
{
"id": "O003-T215",
"native": {
"en": "torus",
"id": "O003-T215",
"id_ID": "torus",
"note": "Standard topology term for the pairwise same-direction quotient of opposite square edges",
"status": "approved"
}
},
{
"id": "O003-T216",
"native": {
"en": "Klein bottle",
"id": "O003-T216",
"id_ID": "botol Klein",
"note": "Standard Indonesian name for the nonorientable quotient surface",
"status": "approved"
}
},
{
"id": "O003-T217",
"native": {
"en": "unit square",
"id": "O003-T217",
"id_ID": "persegi satuan",
"note": "The Cartesian product of the closed unit interval with itself",
"status": "approved"
}
},
{
"id": "O003-T218",
"native": {
"en": "canonical quotient projection",
"id": "O003-T218",
"id_ID": "proyeksi kuosien kanonis",
"note": "Use for the distinguished map sending each point to its equivalence class",
"status": "approved"
}
},
{
"id": "O003-T219",
"native": {
"en": "well-defined",
"id": "O003-T219",
"id_ID": "terdefinisi dengan baik",
"note": "Use when a formula on equivalence classes is independent of the representative",
"status": "approved"
}
},
{
"id": "O003-T220",
"native": {
"en": "respects an equivalence relation",
"id": "O003-T220",
"id_ID": "menghormati relasi ekuivalensi",
"note": "A function has equal values on equivalent points and therefore descends to the quotient",
"status": "approved"
}
},
{
"id": "O003-T221",
"native": {
"en": "open arc",
"id": "O003-T221",
"id_ID": "busur terbuka",
"note": "Use for a basic open connected proper subset of the circle",
"status": "approved"
}
},
{
"id": "O003-T222",
"native": {
"en": "basic open set",
"id": "O003-T222",
"id_ID": "himpunan terbuka basis",
"note": "Reader term for a member of a chosen basis",
"status": "approved"
}
},
{
"id": "O003-T223",
"native": {
"en": "sphere",
"id": "O003-T223",
"id_ID": "permukaan bola",
"note": "Use for the topological sphere and distinguish it from a metric open or closed ball",
"status": "approved"
}
},
{
"id": "O003-T224",
"native": {
"en": "unit disk",
"id": "O003-T224",
"id_ID": "cakram satuan",
"note": "Qualify as cakram satuan tertutup or terbuka when the defining inequality requires it; do not use lingkaran",
"status": "approved"
}
},
{
"id": "O003-T225",
"native": {
"en": "diametrically opposite points; antipodal points",
"id": "O003-T225",
"id_ID": "titik-titik berseberangan secara diametral; titik-titik antipodal",
"note": "Introduce both once and thereafter prefer titik antipodal",
"status": "approved"
}
},
{
"id": "O003-T226",
"native": {
"en": "real projective plane",
"id": "O003-T226",
"id_ID": "bidang proyektif real",
"note": "Align real with the edition's bilangan real usage",
"status": "approved"
}
},
{
"id": "O003-T227",
"native": {
"en": "point at infinity",
"id": "O003-T227",
"id_ID": "titik di tak hingga",
"note": "Preferred natural phrase for an adjoined ideal point",
"status": "approved"
}
},
{
"id": "O003-T228",
"native": {
"en": "hemisphere",
"id": "O003-T228",
"id_ID": "hemisfer",
"note": "At first use optionally gloss as belahan permukaan bola to avoid confusion with a solid half-ball",
"status": "approved"
}
},
{
"id": "O003-T229",
"native": {
"en": "equator",
"id": "O003-T229",
"id_ID": "ekuator",
"note": "Boundary circle shared by the two hemispheres",
"status": "approved"
}
},
{
"id": "O003-T230",
"native": {
"en": "nonorientable",
"id": "O003-T230",
"id_ID": "tak dapat diorientasikan",
"note": "Semantically stronger and safer than tak terorientasi because the latter can merely mean no orientation was chosen",
"status": "approved"
}
},
{
"id": "O003-T231",
"native": {
"en": "connected sum",
"id": "O003-T231",
"id_ID": "jumlah terhubung",
"note": "Use for the surface operation; do not translate as ordinary union",
"status": "approved"
}
},
{
"id": "O003-T232",
"native": {
"en": "closed surface",
"id": "O003-T232",
"id_ID": "permukaan tertutup",
"note": "Closed means compact without boundary in the classification context",
"status": "approved"
}
},
{
"id": "O003-T233",
"native": {
"en": "classification of closed surfaces",
"id": "O003-T233",
"id_ID": "klasifikasi permukaan tertutup",
"note": "Use Teorema Klasifikasi Permukaan Tertutup when naming the theorem",
"status": "approved"
}
},
{
"id": "O003-T234",
"native": {
"en": "retract",
"id": "O003-T234",
"id_ID": "retrak",
"note": "A subspace A that is the image fixed pointwise by a retraction",
"status": "approved"
}
},
{
"id": "O003-T235",
"native": {
"en": "retraction",
"id": "O003-T235",
"id_ID": "retraksi",
"note": "The map r:X to A satisfying its restriction to A equals the identity",
"status": "approved"
}
},
{
"id": "O003-T236",
"native": {
"en": "deformation retract",
"id": "O003-T236",
"id_ID": "retrak deformasi",
"note": "Use A adalah retrak deformasi dari X",
"status": "approved"
}
},
{
"id": "O003-T237",
"native": {
"en": "deformation retraction",
"id": "O003-T237",
"id_ID": "retraksi deformasi",
"note": "Use for the deformation or homotopy realizing a deformation retract",
"status": "approved"
}
},
{
"id": "O003-T238",
"native": {
"en": "attach or adjoin along the boundary",
"id": "O003-T238",
"id_ID": "merekatkan sepanjang batas",
"note": "In a sentence use direkatkan sepanjang batasnya; for adjoin use menambahkan dengan merekatkannya sepanjang batas",
"status": "approved"
}
},
{
"id": "O003-T239",
"native": {
"en": "two-point space",
"id": "O003-T239",
"id_ID": "ruang dua titik",
"note": "Transparent finite-space term",
"status": "approved"
}
},
{
"id": "O003-T240",
"native": {
"en": "largest topology",
"id": "O003-T240",
"id_ID": "topologi terbesar",
"note": "Means largest under inclusion; topologi paling halus is an equivalent explanatory gloss",
"status": "approved"
}
},
{
"id": "O003-T241",
"native": {
"en": "cover",
"id": "O003-T241",
"id_ID": "selimut",
"note": "Use for a family of sets whose union contains the target set; distinct from topological closure or tutupan",
"status": "approved"
}
},
{
"id": "O003-T242",
"native": {
"en": "open cover",
"id": "O003-T242",
"id_ID": "selimut buka",
"note": "Attested in the Universitas Terbuka Pengantar Topologi course overview",
"status": "approved"
}
},
{
"id": "O003-T243",
"native": {
"en": "subcover",
"id": "O003-T243",
"id_ID": "subselimut",
"note": "A subfamily that remains a cover; formed transparently from the attested selimut term",
"status": "approved"
}
},
{
"id": "O003-T244",
"native": {
"en": "finite subcover",
"id": "O003-T244",
"id_ID": "subselimut berhingga",
"note": "A finite subfamily that remains a cover",
"status": "approved"
}
},
{
"id": "O003-T245",
"native": {
"en": "compact subset",
"id": "O003-T245",
"id_ID": "subhimpunan kompak",
"note": "Use for a subset compact in the ambient or subspace context as specified",
"status": "approved"
}
},
{
"id": "O003-T246",
"native": {
"en": "bounded subset",
"id": "O003-T246",
"id_ID": "subhimpunan terbatas",
"note": "Use in Euclidean and metric-space boundedness statements",
"status": "approved"
}
},
{
"id": "O003-T247",
"native": {
"en": "standard n-dimensional cube",
"id": "O003-T247",
"id_ID": "kubus standar berdimensi n",
"note": "Keep n as protected mathematics when it is displayed",
"status": "approved"
}
},
{
"id": "O003-T248",
"native": {
"en": "Heine-Borel theorem",
"id": "O003-T248",
"id_ID": "Teorema Heine-Borel",
"note": "Retain the conventional theorem name",
"status": "approved"
}
},
{
"id": "O003-T249",
"native": {
"en": "finite intersection property",
"id": "O003-T249",
"id_ID": "sifat irisan berhingga",
"note": "Standard compactness-equivalent property for families of closed sets",
"status": "approved"
}
},
{
"id": "O003-T250",
"native": {
"en": "locally compact",
"id": "O003-T250",
"id_ID": "kompak lokal",
"note": "Use as a predicate for a topological space",
"status": "approved"
}
},
{
"id": "O003-T251",
"native": {
"en": "Hausdorff distance",
"id": "O003-T251",
"id_ID": "jarak Hausdorff",
"note": "Use for the symmetric distance between nonempty compact subsets",
"status": "approved"
}
},
{
"id": "O003-T252",
"native": {
"en": "Hausdorff metric",
"id": "O003-T252",
"id_ID": "metrik Hausdorff",
"note": "Use when the Hausdorff distance is treated as a metric",
"status": "approved"
}
},
{
"id": "O003-T253",
"native": {
"en": "iterated function system",
"id": "O003-T253",
"id_ID": "sistem fungsi teriterasi",
"note": "Use for the contraction-based fractal construction",
"status": "approved"
}
},
{
"id": "O003-T254",
"native": {
"en": "attractor",
"id": "O003-T254",
"id_ID": "atraktor",
"note": "Use for the limiting invariant compact set of an iterated function system",
"status": "approved"
}
},
{
"id": "O003-T255",
"native": {
"en": "contraction mapping",
"id": "O003-T255",
"id_ID": "pemetaan kontraksi",
"note": "Use for a map with contraction factor below one",
"status": "approved"
}
},
{
"id": "O003-T256",
"native": {
"en": "contraction factor",
"id": "O003-T256",
"id_ID": "faktor kontraksi",
"note": "Express the scale ratio directly such as one half",
"status": "approved"
}
},
{
"id": "O003-T257",
"native": {
"en": "Cauchy sequence",
"id": "O003-T257",
"id_ID": "barisan Cauchy",
"note": "Retain the mathematician name and Indonesian sequence term",
"status": "approved"
}
},
{
"id": "O003-T258",
"native": {
"en": "complete metric space",
"id": "O003-T258",
"id_ID": "ruang metrik lengkap",
"note": "A metric space in which every Cauchy sequence converges",
"status": "approved"
}
},
{
"id": "O003-T259",
"native": {
"en": "fractal",
"id": "O003-T259",
"id_ID": "fraktal",
"note": "Established Indonesian mathematical spelling",
"status": "approved"
}
},
{
"id": "O003-T260",
"native": {
"en": "Sierpinski triangle",
"id": "O003-T260",
"id_ID": "segitiga Sierpinski",
"note": "Retain the conventional proper name without diacritic normalization",
"status": "approved"
}
},
{
"id": "O003-T400",
"native": {
"en": "box topology",
"id": "O003-T400",
"id_ID": "topologi kotak",
"note": "Use for the topology generated by products of open factor sets in the finite-product setting",
"status": "approved"
}
},
{
"id": "O003-T401",
"native": {
"en": "projection map",
"id": "O003-T401",
"id_ID": "peta proyeksi",
"note": "Use for the canonical map from a product to one factor",
"status": "approved"
}
},
{
"id": "O003-T402",
"native": {
"en": "digital plane",
"id": "O003-T402",
"id_ID": "bidang digital",
"note": "Use for the integer lattice viewed with a digital topology",
"status": "approved"
}
},
{
"id": "O003-T403",
"native": {
"en": "4-neighbor",
"id": "O003-T403",
"id_ID": "tetangga-4",
"note": "Use the numeral after the noun consistently in prose",
"status": "approved"
}
},
{
"id": "O003-T404",
"native": {
"en": "8-neighbor",
"id": "O003-T404",
"id_ID": "tetangga-8",
"note": "Use the numeral after the noun consistently in prose",
"status": "approved"
}
},
{
"id": "O003-T405",
"native": {
"en": "k-path",
"id": "O003-T405",
"id_ID": "lintasan-k",
"note": "Use the parameter after the path noun and retain k as mathematics when marked up",
"status": "approved"
}
},
{
"id": "O003-T406",
"native": {
"en": "k-connected",
"id": "O003-T406",
"id_ID": "terhubung-k",
"note": "Use the parameter after the connectedness adjective and retain k as mathematics when marked up",
"status": "approved"
}
},
{
"id": "O003-T407",
"native": {
"en": "digital Jordan curve",
"id": "O003-T407",
"id_ID": "kurva Jordan digital",
"note": "Retain the proper name Jordan and place digital after the noun phrase",
"status": "approved"
}
},
{
"id": "O003-T408",
"native": {
"en": "Khalimsky topology",
"id": "O003-T408",
"id_ID": "topologi Khalimsky",
"note": "Retain the proper name Khalimsky",
"status": "approved"
}
},
{
"id": "O003-T409",
"native": {
"en": "digital interval",
"id": "O003-T409",
"id_ID": "interval digital",
"note": "Use for an integer interval equipped with the digital-line topology",
"status": "approved"
}
},
{
"id": "O003-T410",
"native": {
"en": "digital path",
"id": "O003-T410",
"id_ID": "lintasan digital",
"note": "Use for the range of a continuous function from a digital interval",
"status": "approved"
}
},
{
"id": "O003-T411",
"native": {
"en": "digital arc",
"id": "O003-T411",
"id_ID": "busur digital",
"note": "Use for the range of a homeomorphism from a digital interval",
"status": "approved"
}
},
{
"id": "O003-T412",
"native": {
"en": "pure point",
"id": "O003-T412",
"id_ID": "titik murni",
"note": "Use for a lattice point whose coordinates have the same parity",
"status": "approved"
}
},
{
"id": "O003-T413",
"native": {
"en": "mixed point",
"id": "O003-T413",
"id_ID": "titik campuran",
"note": "Use for a lattice point whose coordinates have different parity",
"status": "approved"
}
},
{
"id": "O003-T500",
"native": {
"en": "first-countability axiom",
"id": "O003-T500",
"id_ID": "aksioma keterhitungan pertama",
"note": "Primary Indonesian topology-journal usage; distinguish the axiom noun phrase from the predicate for a space",
"status": "approved"
}
},
{
"id": "O003-T501",
"native": {
"en": "first-countable space",
"id": "O003-T501",
"id_ID": "ruang terhitung pertama",
"note": "Primary Indonesian topology-journal usage; use terhitung rather than the earlier unsubstantiated berketerhitungan form",
"status": "approved"
}
},
{
"id": "O003-T502",
"native": {
"en": "second-countability axiom",
"id": "O003-T502",
"id_ID": "aksioma keterhitungan kedua",
"note": "Parallel transparent form for the axiom that the topology has a countable basis",
"status": "approved"
}
},
{
"id": "O003-T503",
"native": {
"en": "second-countable space",
"id": "O003-T503",
"id_ID": "ruang terhitung kedua",
"note": "Predicate form parallel to attested ruang terhitung pertama",
"status": "approved"
}
},
{
"id": "O003-T504",
"native": {
"en": "net",
"id": "O003-T504",
"id_ID": "jaring",
"note": "Use the Indonesian mathematical noun throughout reader-visible prose; retain locale-neutral IDs and source locators",
"status": "approved"
}
},
{
"id": "O003-T505",
"native": {
"en": "subnet",
"id": "O003-T505",
"id_ID": "subjaring",
"note": "Derived consistently from jaring and used for Kelley subnets",
"status": "approved"
}
},
{
"id": "O003-T506",
"native": {
"en": "directed set",
"id": "O003-T506",
"id_ID": "himpunan terarah",
"note": "Index set for a net with the direction relation made explicit",
"status": "approved"
}
},
{
"id": "O003-T507",
"native": {
"en": "cluster point",
"id": "O003-T507",
"id_ID": "titik gugus",
"note": "Use for a point at which a net is frequently eventually-near; distinguish from limit point when context matters",
"status": "approved"
}
},
{
"id": "O003-T508",
"native": {
"en": "specialization preorder",
"id": "O003-T508",
"id_ID": "praurutan spesialisasi",
"note": "Use for x less than or equal to y when every open neighborhood of x contains y",
"status": "approved"
}
},
{
"id": "O003-T509",
"native": {
"en": "Kolmogorov quotient",
"id": "O003-T509",
"id_ID": "kuosien Kolmogorov",
"note": "Retain the proper name and established kuosien spelling",
"status": "approved"
}
},
{
"id": "O003-T510",
"native": {
"en": "completely regular",
"id": "O003-T510",
"id_ID": "reguler lengkap",
"note": "Use with the explicit point-versus-closed-set function-separation definition",
"status": "approved"
}
},
{
"id": "O003-T511",
"native": {
"_extra_columns": [
"Y) with subbasis [K",
"U]"
],
"en": "compact-open topology",
"id": "O003-T511",
"id_ID": "topologi kompak-terbuka",
"note": "Use for the topology on C(X",
"status": "approved"
}
},
{
"id": "O003-T512",
"native": {
"en": "one-point compactification",
"id": "O003-T512",
"id_ID": "kompaktifikasi satu titik",
"note": "Use for the Alexandroff compactification of a noncompact locally compact Hausdorff space",
"status": "approved"
}
},
{
"id": "O003-T513",
"native": {
"en": "pseudometric",
"id": "O003-T513",
"id_ID": "pseudometrik",
"note": "Use when distinct points may have distance zero",
"status": "approved"
}
},
{
"id": "O003-T514",
"native": {
"en": "metrization",
"id": "O003-T514",
"id_ID": "metrisasi",
"note": "Use for construction or existence of a metric inducing the given topology",
"status": "approved"
}
},
{
"id": "O003-T515",
"native": {
"en": "equicontinuous",
"id": "O003-T515",
"id_ID": "ekukontinu",
"note": "Use for a function family sharing the required local continuity control",
"status": "approved"
}
},
{
"id": "O003-T516",
"native": {
"en": "pointwise convergence",
"id": "O003-T516",
"id_ID": "kekonvergenan titik demi titik",
"note": "Use for convergence in the product topology on a function space",
"status": "approved"
}
},
{
"id": "O003-T517",
"native": {
"en": "uniform topology",
"id": "O003-T517",
"id_ID": "topologi seragam",
"note": "Use only when the codomain carries a metric or uniform structure",
"status": "approved"
}
},
{
"id": "O003-T518",
"native": {
"en": "function space",
"id": "O003-T518",
"id_ID": "ruang fungsi",
"note": "Use for a set of functions equipped with a specified topology",
"status": "approved"
}
},
{
"id": "O003-T519",
"native": {
"en": "Lindelof space",
"id": "O003-T519",
"id_ID": "ruang Lindelöf",
"note": "Retain the proper-name diacritic and state the countable-subcover property",
"status": "approved"
}
},
{
"id": "O003-T520",
"native": {
"en": "separable space",
"id": "O003-T520",
"id_ID": "ruang separabel",
"note": "Use for a space with a countable dense subset",
"status": "approved"
}
},
{
"id": "O003-T521",
"native": {
"en": "bicontinuous",
"id": "O003-T521",
"id_ID": "dwikontinu",
"note": "Official UNDIP Buku Ajar Topologi synopsis attests dwikontinu; use only when both a map and its inverse are continuous",
"status": "approved"
}
},
{
"id": "O003-T522",
"native": {
"en": "one-to-one correspondence",
"id": "O003-T522",
"id_ID": "korespondensi satu-satu",
"note": "Attested in the indexed opening learning outcome for official UT Pengantar Topologi Module 1 and already used naturally in the edition",
"status": "approved"
}
},
{
"id": "O003-T523",
"native": {
"en": "partial order",
"id": "O003-T523",
"id_ID": "urutan parsial",
"note": "Use for a reflexive antisymmetric transitive order relation",
"status": "approved"
}
},
{
"id": "O003-T524",
"native": {
"en": "partially ordered set",
"id": "O003-T524",
"id_ID": "himpunan terurut parsial",
"note": "Attested in the indexed opening learning outcome for official UT Pengantar Topologi Module 1",
"status": "approved"
}
}
]
}