Let $X$ be Hausdorff. There is a Theorem:
If the closure of every discrete subspace of $X$ is $H$-closed, then $X$ is compact.
(A topological space $X$ is said to be $H$-closed, or Hausdorff closed, or absolutely closed if it is closed in every Hausdorff space space containing it as a subspace. This property is a generalization of compactness, since a compact subset of a Hausdorff space is closed. Thus, every compact Hausdorff space is H-closed. The notion of an $H$-closed space has been introduced in 1924 by P. Alexandroff and P. Urysohn.)
In the process of prove, author said it is easy to see that $X$ is countably compact. However, I find it is difficult for me to get it. My question is this, just as the title explains:
How could I easily see that such space is countably compact？