Countable Fort Space is Perfectly Normal

Theorem
Let $T = \left({S, \tau_p}\right)$ be a Fort space on a countably infinite set $S$.

Then $T$ is a perfectly normal space.

Proof
We have from Closed Set of Countable Fort Space is G-Delta that every closed set in $T$ is a $G_\delta$ set.

From Fort Space is T5 and T5 Space is T4 Space, we have that a Fort space is a $T_4$.

From Fort Space is T1 it follows by definition that $T$ is a perfectly normal space.