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 one set.

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

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