\begin{definition}[Definition:Compact Space/Topology/Subspace/Definition 2]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a subset of $S$.
$H$ is '''compact in $T$''' {{iff}} every open cover $\CC \subseteq \tau$ for $H$ has a finite subcover.
\end{definition}