Definition:Relatively Closed Set

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 $C \cap B = A$.