Adjusted citation formats. Moved citation off of named theorems if possible.
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Bokuan Li
2026-03-19 23:58:16 -04:00
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@@ -35,11 +35,11 @@
so $V = \bigcup_{j = 1}^n V_{x_j} \in \cn^o(K)$ is precompact.
\end{proof}
\begin{lemma}[Urysohn's Lemma (LCH), {{\cite[Lemma 4.32]{Folland}}}]
\begin{lemma}[Urysohn's Lemma (LCH)]
\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 $\supp{f} \subset U$.
\end{lemma}
\begin{proof}
\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
\[
K \subset V \subset \ol{V} \subset W \subset \ol{W} \subset U