Fixed regex incident.
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This commit is contained in:
Bokuan Li
2026-05-05 02:00:05 -04:00
parent 0f2e69d1f9
commit 97372173e1
78 changed files with 172 additions and 172 deletions

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@@ -8,7 +8,7 @@
\item For any $x \in X$, there exists $K \in \cn(x)$ compact.
\item For any $x \in X$, $\cn(x)$ admits a fundamental system of neighbourhoods consisting of compact sets.
\item For any $x \in X$, $\cn(x)$ admits a fundamental system of neighbourhoods consisting of precompact sets.
\end\{enumerate\}
\end{enumerate}
If the above holds, then $X$ is a \textbf{locally compact Hausdorff (LCH)} space.
\end{definition}
@@ -122,7 +122,7 @@
\item[(a)] For each $0 \le k \le n$, $U_k$ is a precompact open set.
\item[(b)] For each $0 \le k < n$, $\overline{U_k} \subset U_{k+1}$.
\item[(c)] For each $1 \le k \le n$, $U_k \supset \bigcup_{j = 1}^k K_j$.
\end\{enumerate\}
\end{enumerate}
By \autoref{lemma:lch-compact-neighbour}, there exists $U_{n+1} \in \cn^o(\overline{U_n} \cup K_{n+1})$ precompact. In which case, by (c),
\[
@@ -185,7 +185,7 @@
\begin{enumerate}
\item[(a)] $\ol{E} \subset \bigcup_{x \in X_E}N_x$.
\item[(b)] For every $x \in X_E$, $N_x \cap E \ne \emptyset$.
\end\{enumerate\}
\end{enumerate}
Let $X_{\ce} = \bigcup_{E \in \ce}X_\ce$, and for each $E \in \ce$, let
\[