fix typos

content/Math4201/Math4201_L32.md

@@ -30,7 +30,7 @@ First, we prove that $X$ is a subspace of $Y$. (That is, every open set $U\subse
 
 Case 1: $U\subseteq X$ is open in $X$, then $U\cap X=U$ is open in $Y$.
 
-Case 2: $\infty\in U$, then $Y-U$ is a compact subspace of $X$, since $X$ is Hausdorff. So $Y-U$ is a closed subspace of $X$.
+Case 2: $\infty\in U$, then $Y-U$ is a compact subspace of $X$. Since $X$ is Hausdorff, $Y-U$ is a closed subspace of $X$. [Compact subspace of a Hausdorff space is closed](../Math4201_L25#proposition-of-compact-subspaces-with-hausdorff-property)
 
 So $X\cap U=X-(Y-U)$ is open in $X$.