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Minor adjustments.

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Bokuan Li
2026-01-22 19:02:42 -05:00
parent 234f158663
commit e847ead004
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src/topology/main/quotient.tex
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@@ -26,8 +26,8 @@
Let $X$ be a topological space, $\sim$ be an equivalence relation on $X$, then there exists $(\td X, \pi)$ such that: Let $X$ be a topological space, $\sim$ be an equivalence relation on $X$, then there exists $(\td X, \pi)$ such that:
\begin{enumerate} \begin{enumerate}
\item $\td X$ is a topological space with ground set $X/\sim$. \item $\td X$ is a topological space with ground set $X/\sim$.
\item $\pi$ is constant on each equivalence class of $\sim$.
\item $\pi \in C(X; \td X)$. \item $\pi \in C(X; \td X)$.
\item $\pi$ is constant on each equivalence class of $\sim$.
\item[(U)] For any pair $(Y, f)$ satisfying (1), (2), and (3), there exists a unique $\td f \in C(\td X; Y)$ such that the following diagram commutes: \item[(U)] For any pair $(Y, f)$ satisfying (1), (2), and (3), there exists a unique $\td f \in C(\td X; Y)$ such that the following diagram commutes:
\[ \[
\xymatrix{ \xymatrix{