Non-Trivial Particular Point Topology is not T1

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

Then $T$ is not a $T_1$ (Fréchet) space.

Proof
Follows directly from:


 * Particular Point Topology is Closed Extension Topology of Discrete Topology
 * Closed Extension Topology is not $T_1$.