Sierpiński Space is T5

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

Then $T$ is a $T_5$ space.

Proof
The only closed sets in $T$ are $\O$, $\set 1$ and $\set {0, 1}$.

So there are no two separated sets $A, B \subseteq \set {0, 1}$.

So $T$ is a $T_5$ space vacuously.