\begin{definition}[Definition:Excluded Point Topology/Countable]
Let $S$ be a set which is non-empty.
Let $p \in S$ be some '''particular point''' of $S$.
Let $T = \struct {S, \tau_{\bar p} }$ be the excluded point space on $S$ by $p$. 
Let $S$ be countably infinite.
Then $\tau_{\bar p}$ is a '''countable excluded point topology''', and $\struct {S, \tau_{\bar p} }$ is a '''countable excluded point space'''.
\end{definition}