Definition:Relatively Closed Set

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

Let $A \subseteq B \subseteq S$.

Then $A$ is relatively closed in $B$ iff $A$ is closed in the relative topology of $B$.

Also see
Equivalently, $A$ is relatively closed in $B$ iff there is a closed set $C \subseteq S$ with $C \cap B = A$.

This is proved in Relatively Closed by Intersection with Closed Set.