Definition:Relatively Closed Set/Definition 2

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq B \subseteq S$.

$A$ is relatively closed in $B$ there is a closed set $C \subseteq S$ with $C \cap B = A$.

Also see

 * Equivalence of Definitions of Relatively Closed Set