Definition:Limit Point/Metric Space/Definition 3

Definition
Let $M = \struct {S, d}$ be a metric space.

Let $\tau$ be the topology induced by the metric $d$.

Let $A \subseteq S$ be a subset of $S$.

Let $\alpha \in S$.

$\alpha$ is a limit point of $A$ $\alpha$ is a limit point in the topological space $\struct{S, \tau}$.

Also see

 * Equivalence of Definitions of Limit Point in Metric Space