Let $X$ be Lindelöf and let $A \subseteq X$ be closed. Show that it follows that $A$ is Lindelöf.
That is, we want to show for every open cover of $A$, there is a countable subcover.
Note: (A space is Lindelöf if every open cover of the space has a countable subcover, a weakening of the better-known notion of compactess).