Non-Trivial Excluded Point Topology is not T1

Theorem
Let $T = \left({S, \vartheta_p}\right)$ be a excluded point space such that $S$ is not a singleton.

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

Proof
Follows directly from:


 * Excluded Point Topology is Open Extension Topology of Discrete Topology


 * Open Extension Topology is Not $T_1$