Sigma-compactness

In topology, a σ-compact space is a topological space that is the union of countably many compact subsets. Obviously, every compact space is σ-compact. Moreover, every σ-compact space is Lindelöf (i.e. every open cover has a countable subcover). The reverse implications do not hold. For example, standard Euclidean space (Rⁿ) is σ-compact but not compact, and the lower limit topology on the real line is Lindelöf but not σ-compact or compact.

A space is σ-locally compact if it is both σ-compact and locally compact.