Closed Set is F-Sigma Set

Theorem
Let $\left({X, \vartheta}\right)$ be a topological space.

Let $V$ be a closed set of $X$.

Then $V$ is an $F_\sigma$ set of $X$.

Proof
$V$ is the union of a singleton.

So $V$ is trivially the union of a countable number of closed sets of $X$.

The result follows by definition of $F_\sigma$ set.