Pemeriksaan P.2. Memeriksa Topologi Kuosien Berhingga.
Gunakan \(X\text{,}\) \(Y\text{,}\) \(p\text{,}\) dan \(\tau\) berikut: \(X=\{1,2,3,4,5,6\}\text{,}\) \(Y=\{a,b,c,d\}\text{,}\)
\begin{equation*}
\tau=\{\emptyset,\{1,2\},\{4,6\},\{1,2,4,6\},X\},
\end{equation*}
serta \(p(1)=b\text{,}\) \(p(2)=a\text{,}\) \(p(3)=c\text{,}\) \(p(4)=d\text{,}\) \(p(5)=c\text{,}\) dan \(p(6)=a\text{.}\) Buktikan bahwa \(\sigma=\{U\subseteq Y\mid p^{-1}(U)\in\tau\}\) merupakan topologi pada \(Y\text{.}\)