\begin{definition}[Definition:Isolated Point (Topology)/Subset/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a subset of $S$.
$x \in H$ is an '''isolated point of $H$''' {{iff}}:
:$\exists U \in \tau: U \cap H  = \set x$
That is, {{iff}} there exists an open set of $T$ containing no points of $H$ other than $x$.
\end{definition}