Indiscrete Space is T5

Theorem
Let $T = \struct {S, \set {\O, S} }$ be an indiscrete topological space.

Then $T$ is a $T_5$ space.

Proof
By definition, the only two separated sets in $T$ are $S$ and $\O$.

Then there exist two disjoint open sets $S$ and $\O$ containing $S$ and $\O$ respectively.

Hence (trivially) $T$ is a $T_5$ space.