\begin{definition}[Definition:Isolated Point (Metric Space)/Subset]
Let $M = \struct {A, d}$ be a metric space.
Let $S \subseteq A$ be a subset of $A$.
$a \in S$ is an '''isolated point''' of $S$ {{iff}} there exists an open $\epsilon$-ball of $x$ in $M$ containing no points of $S$ other than $a$:
:$\exists \epsilon \in \R_{>0}: \map {B_\epsilon} a \cap S = \set a$
That is:
:$\exists \epsilon \in \R_{>0}: \set {x \in S: \map d {x, a} < \epsilon} = \set a$
\end{definition}