T0 Space is not necessarily T1 Space/Proof 2

Proof
Proof by Counterexample:

Let $T$ be the overlapping interval space.

From Existence of Topological Space which satisfies no Separation Axioms but $T_0$, we have that:
 * $T$ is a $T_0$ space

but:
 * $T$ is not a $T_1$ space.

The result follows.