diff --git a/src/topology/main/lch.tex b/src/topology/main/lch.tex
index 56c6b6a..1f8f19c 100644
--- a/src/topology/main/lch.tex
+++ b/src/topology/main/lch.tex
@@ -159,7 +159,7 @@
 \end{proof}
 
 \begin{lemma}
-\label{lemma:lch-locally-finite-relatively compact-refine}
+\label{lemma:lch-locally-finite-relatively-compact-refine}
     Let $X$ be a LCH space and $\ce \subset 2^X$ be a locally finite relatively compact open cover of $X$, then there exists locally finite relatively compact open covers $\bracs{F_E}_{E \in \ce}, \bracs{G_E}_{E \in \ce} \subset 2^X$ such that for each $E \in \ce$, $G_E \subset \ol{G_E} \subset E \subset \ol{E} \subset F_E$.
 \end{lemma}
 \begin{proof}
@@ -223,7 +223,7 @@
 \begin{proof}
     (1) $\Rightarrow$ (2): For each $x \in X$, there exists a relatively compact open neighbourhood $U_x \in \cn^o(x)$. Since $\bracs{U_x| x \in X}$ is an open cover of $X$, there exists a locally finite refinement $\mathcal{V}$. For each $V \in \mathcal{V}$, there exists $x \in X$ such that $V \subset U_x$. In which case, $\ol{V} \subset \ol{U_x}$ is compact.
 
-    (2) $\Rightarrow$ (3): Let $\cf \subset 2^X$ be a locally finite open cover of $X$ consisting of relatively compact open sets. By \autoref{lemma:lch-locally-finite-relatively compact-refine}, there exists a locally finite open cover $\bracs{G_F}_{F \in \cf}$ of $X$ consisting of relatively compact open sets such that $\ol{F} \subset G_F$ for all $F \in \cf$.
+    (2) $\Rightarrow$ (3): Let $\cf \subset 2^X$ be a locally finite open cover of $X$ consisting of relatively compact open sets. By \autoref{lemma:lch-locally-finite-relatively-compact-refine}, there exists a locally finite open cover $\bracs{G_F}_{F \in \cf}$ of $X$ consisting of relatively compact open sets such that $\ol{F} \subset G_F$ for all $F \in \cf$.
 
     For each $F \in \cf$, let
     \[
@@ -239,7 +239,7 @@
 
     is finite, and $\mathcal{V}$ is locally finite.
 
-    (3) $\Rightarrow$ (4): By \autoref{lemma:lch-locally-finite-relatively compact-refine}.
+    (3) $\Rightarrow$ (4): By \autoref{lemma:lch-locally-finite-relatively-compact-refine}.
 
     (4) $\Rightarrow$ (5): Let $\seqi{V}, \seqi{W} \subset 2^X$ be locally finite refinements of $\mathcal{U}$ consisting of relatively compact open sets such that for each $i \in I$, $\ol{W_i} \subset V_i$.