Closed Sets of Fortissimo Space

Theorem

Let $T = \struct {S, \tau_p}$ be a Fortissimo space.

Then $H \subseteq S$ is closed in $T$ if and only if:

$p \in H$

or

$H$ is countable

or both.

Proof

By definition of a Fortissimo space, $U \subseteq S$ is open in $T$ if and only if:

$p \in \relcomp S U$

or

$\relcomp S U$ is countable

or both.

The result follows from the definition of closed set.

$\blacksquare$