T0 Space is not necessarily T1 Space/Proof 1

Proof
Proof by Counterexample:

Let $T = \struct {S, \tau_p}$ be a particular point space such that $S$ is not a singleton.

From Particular Point Space is $T_0$, we have that $T$ is a $T_0$ space.

From Non-Trivial Particular Point Topology is not $T_1$, $T$ is not a $T_1$ space.

The result follows.