Definition:Excluded Point Topology/Countable

Definition
Let $S$ be a set which is non-empty.

Let $p \in S$ be some particular point of $S$.

Let $T = \left({S, \tau_{\bar p}}\right)$ 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 $\left({S, \tau_{\bar p}}\right)$ is a countable excluded point space.