Countable Complement Space is not T2

Theorem
Let $T = \left({S, \tau}\right)$ be a countable complement topology on an uncountable set $S$.

Then $T$ is not a $T_2$ (Hausdorff) space.

Proof
We have:
 * Countable Complement Space is Irreducible
 * Irreducible Hausdorff Space is Singleton