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