Polished A-A and added new lines for broken enumerates.

src/topology/uniform/equicontinuous.tex

@@ -66,4 +66,19 @@
 \end{proof}
 
 
+\begin{corollary}
+\label{corollary:arzela-locally-compact}
+    Let $X$ be a LCH space, $Y$ be a uniform space, and $\cf \subset C(X; Y)$ such that:
+    \begin{enumerate}[label=(E\arabic*)]
+        \item $\cf$ is equicontinuous.
+        \item For each $x \in X$, $\cf(x) = \bracs{f(x)|f \in \cf}$ is precompact in $Y$.
+    \end{enumerate}
+
+    then $\cf$ is a precompact subset of $C(X; Y)$ with respect to the compact uniformity. 
+\end{corollary}
+\begin{proof}
+    By the \hyperref[Arzelà-Ascoli Theorem]{theorem:arzela-ascoli}, $\cf$ is a precompact subset of $Y^X$. By \autoref{proposition:lch-compactly-generated}, $C(X; Y)$ is a closed subset of $Y^X$. Therefore $\cf$ is a precompact subset of $C(X; Y)$. 
+\end{proof}
+
+