Definition:Relatively Compact Subspace

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

Let $T_H = \left({H, \tau_H}\right)$ be a subspace of $T$.

Let $\operatorname{cl} \left({H}\right)$ be the closure of $H$ in $T$.

Then $T_H$ is relatively compact in $T$ $\operatorname{cl} \left({H}\right)$ is compact.