Definition:Closed Set/Topology/Definition 2
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
$H$ is closed (in $T$) if and only if every limit point of $H$ is also a point of $H$.
That is, by the definition of the derived set:
- $H$ is closed (in $T$) if and only if $H' \subseteq H$
where $H'$ denotes the derived set of $H$.
Also see
- Results about closed sets can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): closed set (of points)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): closed set (of points)