Definition:Limit Point/Metric Space/Definition 2

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 $A$ if and only if there is a sequence $\sequence{\alpha_n}$ in $A \setminus \set \alpha$ such that $\sequence{\alpha_n}$ converges to $\alpha$, that is, $\alpha$ is a limit of the sequence $\sequence{\alpha_n}$ in $S$.

Also see

• Equivalence of Definitions of Limit Point in Metric Space

• Results about limit points in metric spaces can be found here.