\begin{definition}[Definition:Compact Space/Topology/Subspace/Definition 1]
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $H \subseteq S$ be a subset of $S$.
The topological subspace $T_H = \left({H, \tau_H}\right)$ is '''compact in $T$''' {{iff}} $T_H$ is itself a compact topological space.
\end{definition}