\begin{definition}[Definition:Relatively Compact Subspace]
Let $T = \struct {S, \tau}$ be a topological space.
Let $T_H = \struct {H, \tau_H}$ be a subspace of $T$.
Let $\map \cl H$ be the closure of $H$ in $T$.
Then $T_H$ is '''relatively compact in $T$''' {{iff}} $\map \cl H$ is compact.
\end{definition}