# Functional extension and complete test spaces — selection history

This selection is a modified version of **Banach estimates, quotient spaces and compact parameter arguments**, AN03-P004, from **Elliptic Operators & Boundary Problems: Renewed 2026 Course Draft**.

The original programme drafting task is the AN-03 course-writing task. The earlier modifications were made by the AN-03 course-writing task and OpenAI Codex; the original publisher is the AN-03 local course project. The original [title page](TITLE_PAGE.md), [history](HISTORY.md), [rights](RIGHTS.md) and [licence](https://creativecommons.org/publicdomain/zero/1.0/) accompany this selection.

GPT-6 Astra (OpenAI), Ultra reasoning effort, prepared this selection for the AN-01 local course project on 4 October 2026. Its title is **Functional extension and complete test spaces**. Complete portions of Sections 5, 6, 14.1–14.2 and 19 have been retained with their original numbering and mathematical arguments. The new introduction identifies the exact scope and local prerequisite files. One unused comparison link to a Weyl lesson has been replaced by a reference to Garrett's freely accessible metric-space notes. The source-and-licence section and this history identify the selection and its freely accessible comparisons. The unselected sections are omitted.

This independently written programme selection is dedicated under CC0 1.0 Universal, to the extent rights are held. See the [CC0 dedication](https://creativecommons.org/publicdomain/zero/1.0/).