\begin{definition}[Definition:Particular Point Topology/Infinite]
Let $S$ be a set which is non-empty.
Let $p \in S$ be some '''particular point''' of $S$.
Let $T = \left({S, \tau_p}\right)$ be the particular point space on $S$ by $p$. 
Let $S$ be infinite.
Then $\tau_p$ is an '''infinite particular point topology''', and $\left({S, \tau_p}\right)$ is an '''infinite particular point space'''.
\end{definition}