Definition:Compact Space/Topology/Subspace/Definition 2

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

Let $H \subseteq S$ be a subset of $S$.

$H$ is compact in $T$ if and only if every open cover $\mathcal C \subseteq \tau$ for $H$ has a finite subcover.

Also see

  • Results about compact spaces can be found here.