\begin{definition}[Definition:Particular Point Topology]
Let $S$ be a set which is non-empty.
Let $p \in S$ be some '''particular point''' of $S$.
We define a subset $\tau_p$ of the power set $\powerset S$ as:
:$\tau_p = \set {A \subseteq S: p \in A} \cup \set \O$
that is, all the subsets of $S$ which include $p$, along with the empty set.
Then $\tau_p$ is a topology called the '''particular point topology on $S$ by $p$''', or just '''a particular point topology'''.
The topological space $T = \struct {S, \tau_p}$ is called the '''particular point space on $S$ by $p$''', or just '''a particular point space'''.
\end{definition}