Talk:Intersection of Closed Set with Compact Subspace is Compact/Proof 2

$K$ instead of $H$

I believe it should be:


 * Hence $\family {U_\alpha} \cup S \setminus H$ is an open cover of $K$.

Rather than "open cover of $H$". This is because $S\setminus H$ by definition excludes $H$.

And:


 * It follows by definition that a finite subcover:


 * $\set {U_{\alpha_1}, U_{\alpha_2}, \ldots, U_{\alpha_n}, S \setminus H}$


 * of $K$ exists.

Rather than "of $H$ exists". This is because $K$ is compact, yielding the finite subcover.