# Indiscrete Space is T4

## Theorem

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

Then $T$ is a $T_4$ space.

## Proof

We have that an indiscrete space is a $T_5$ space.

Then we have that a $T_5$ Space is a $T_4$ Space.

$\blacksquare$