Definition:Isolated Point (Metric Space)

Definition
Let $M = \left({A, d}\right)$ be a metric space.

Isolated Point in Space
When $S = A$ this reduces to:

Metric Space as a Topological Space
From Metric Induces Topology we can consider the topology $\tau{\left({A, d}\right)}$ on $A$:
 * $\tau{\left({A, d}\right)} := \left\{{B_\epsilon \left({a}\right): \epsilon \in \R_{>0}, a \in A, B_\epsilon \left({a}\right) \subseteq S}\right\}$

and see that the definition given here is compatible with that of the definition for a topological space.