\begin{definition}[Definition:Finite Complement Topology/Countable]
Let $S$ be an infinite set.
Let $\tau$ be the finite complement topology on $S$.
Let $S$ be countably infinite.
Then $\tau$ is a '''finite complement topology on a countable space''', and $\struct {S, \tau}$ is a '''countable finite complement space'''.
\end{definition}