Definition:Closed Set/Metric Space
< Definition:Closed Set(Redirected from Definition:Closed Set of Metric Space)
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Definition
Let $M = \left({A, d}\right)$ be a metric space.
Let $H \subseteq A$.
Definition 1
$H$ is closed (in $M$) if and only if its complement $A \setminus H$ is open in $M$.
Definition 2
$H$ is closed (in $M$) if and only if every limit point of $H$ is also a point of $H$.
Also see
- Results about closed sets can be found here.