\begin{definition}[Definition:Discrete Topology/Infinite]
Let $S \ne \O$ be a set.
Let $\tau = \powerset S$ be the power set of $S$.
That is, let $\tau$ be the set of all subsets of $S$:
:$\tau := \set {H: H \subseteq S}$
Let $S$ be an infinite set.
Then $\tau = \powerset S$ is an '''infinite discrete topology''', and $\struct {S, \tau} = \struct {S, \powerset S}$ is an '''infinite discrete space'''.
\end{definition}