# Countable Complement Space is Not Weakly Countably Compact

## Theorem

Let $T = \left({S, \tau}\right)$ be a countable complement topology on an uncountable set $S$.

Then $T$ is not weakly countably compact.

## Proof

From Limit Points of Countable Complement Space, if $H \subseteq S$ is countable, it contains all its limit points.