In mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces.
[1] A space is said to be σ-locally compact if it is both σ-compact and (weakly) locally compact.
[2] That terminology can be somewhat confusing as it does not fit the usual pattern of σ-(property) meaning a countable union of spaces satisfying (property); that's why such spaces are more commonly referred to explicitly as σ-compact (weakly) locally compact, which is also equivalent to being exhaustible by compact sets.
[3]