From 15dec0e93f240adbb3e60e43ba0eb2ca53405f87 Mon Sep 17 00:00:00 2001 From: Bokuan Li Date: Tue, 23 Jun 2026 15:11:01 -0400 Subject: [PATCH] Fixed typo in LCH. --- src/topology/main/lch.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/topology/main/lch.tex b/src/topology/main/lch.tex index b8f148b..72c8d52 100644 --- a/src/topology/main/lch.tex +++ b/src/topology/main/lch.tex @@ -48,7 +48,7 @@ As $\ol{W}$ is compact, it is normal by \autoref{proposition:compact-hausdorff-normal}. Since $X$ is Hausdorff, $K \subset \ol{W}$ is closed by \autoref{proposition:compact-closed}. - By \hyperref[Urysohn's lemma]{lemma:urysohn}, there exists $f \in C(\ol{V}; [0, 1])$ such that $f|_K = 1$ and $f|_{\ol{W} \setminus V} = 0$. Let + By \hyperref[Urysohn's lemma]{lemma:urysohn}, there exists $f \in C(\ol{W}; [0, 1])$ such that $f|_K = 1$ and $f|_{\ol{W} \setminus V} = 0$. Let \[ F: X \to [0, 1] \quad x \mapsto \begin{cases} f(x) &x \in W \\