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Minor style adjustment in Urysohn.

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Bokuan Li
2026-06-23 19:40:45 -04:00
parent 15dec0e93f
commit aa928717d0
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src/topology/main/lch.tex
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@@ -38,7 +38,7 @@
\begin{lemma}[Urysohn's Lemma (LCH)] \begin{lemma}[Urysohn's Lemma (LCH)]
\label{lemma:lch-urysohn} \label{lemma:lch-urysohn}
Let $X$ be a LCH space, $K \subset X$ be compact, and $U \in \cn(K)$, then there exists $f \in C_c(X; [0, 1])$ such that $\supp{f} \subset U$. Let $X$ be a LCH space, $K \subset X$ be compact, and $U \in \cn(K)$, then there exists $F \in C_c(X; [0, 1])$ such that $\supp{F} \subset U$.
\end{lemma} \end{lemma}
\begin{proof}[Proof, {{\cite[Lemma 4.32]{Folland}}}. ] \begin{proof}[Proof, {{\cite[Lemma 4.32]{Folland}}}. ]
By \autoref{lemma:lch-compact-neighbour}, there exists $V, W \in \cn^o(K)$ precompact such that By \autoref{lemma:lch-compact-neighbour}, there exists $V, W \in \cn^o(K)$ precompact such that