\begin{definition}[Definition:Sigma-Compact Space]
Let $T = \struct {S, \tau}$ be a topological space.
$T$ is '''$\sigma$-compact''' {{iff}} $S$ is the union of the underlying sets of countably many compact subspaces of $T$.
This can be expressed more efficiently as:
$T$ is '''$\sigma$-compact''' {{iff}} it is the union of countably many compact subspaces.
\end{definition}