Fort Space is Compact

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

Then $T$ is a compact space.

Proof
Let $\mathcal C$ be an open cover of $T$.

Let $p \in S$ be the particular point defining the particular point space part of $T$.

Then $\exists U \in \mathcal C$ such that $p \in U$ and so $\complement_S \left({U}\right)$ is finite.

So $U$, together with an open neighborhood of each of the elements of $\complement_S \left({U}\right)$, is a finite subcover of $\mathcal C$.

Hence the result by definition of compact space.