Definition:Isolated Point (Metric Space)/Subset

Definition
Let $M = \left({A, d}\right)$ 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 $a$:
 * $\exists \epsilon \in \R_{>0}: B_\epsilon \left({a}\right) \cap S = \left\{{a}\right\}$

That is:
 * $\exists \epsilon \in \R_{>0}: \left\{{x \in S: d \left({x, a}\right) < \epsilon}\right\} = \left\{{a}\right\}$