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