Definition:Relatively Closed Set
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Definition
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $A \subseteq B \subseteq S$.
Definition 1
$A$ is relatively closed in $B$ if and only if $A$ is closed in the relative topology of $B$.
Definition 2
$A$ is relatively closed in $B$ if and only if there is a closed set $C \subseteq S$ with $C \cap B = A$.