# Closed Set is F-Sigma Set

## Theorem

Let $T = \struct {S, \tau}$ be a topological space.

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

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

## Proof

$V$ is the union of a singleton.

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

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

$\blacksquare$