Closed Sets of Fortissimo Space

Theorem
Let $T = \left({S, \tau_p}\right)$ be a Fortissimo space.

Then $H \subseteq S$ is closed in $T$ iff:
 * $p \in H$

or
 * $H$ is countable

or both.

Proof
By definition of a Fortissimo space, $U \subseteq S$ is open in $T$ iff:
 * $p \in \complement_S \left({U}\right)$

or
 * $\complement_S \left({U}\right)$ is countable

or both.

The result follows from the definition of closed set.