Definition:Closed Set/Metric Space/Definition 2

Definition

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

Let $H \subseteq A$.

$H$ is closed (in $M$) if and only if every limit point of $H$ is also a point of $H$.

Also see

• Equivalence of Definitions of Closed Set in Metric Space

• Results about closed sets can be found here.