Definition:Closed Set/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.