F-Sigma Sets in Indiscrete Topology

Theorem
Let $T = \left({S, \left\{{\varnothing, S}\right\}}\right)$ be an indiscrete topological space.

Let $H \subseteq S$.

$H$ is an $F_\sigma$ (F-sigma) set of $T$ either $H = S$ or $H = \varnothing$.

Proof
An $F_\sigma$ set is a set which can be written as a countable union of closed sets of $S$.

Hence the only $F_\sigma$ sets of $T$ are made from unions of $T$ and $\varnothing$.

So $T$ and $\varnothing$ are the only $F_\sigma$ sets of $T$.