# Sierpiński Space is T4

## Theorem

Let $T = \struct {\set {0, 1}, \tau_0}$ be a Sierpiński space.

Then $T$ is a $T_4$ space.

## Proof

We have that the Sierpiński Space is $T_5$.

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

$\blacksquare$