Definition:Weakly Sigma-Locally Compact Space

Definition
Let $T = \left({X, \vartheta}\right)$ be a topological space.

Then $T$ is $\sigma$-locally compact iff:
 * $T$ is $\sigma$-compact
 * $T$ is locally compact.

That is, $T$ is $\sigma$-locally compact iff:
 * it is the union of countably many compact sets
 * every point of $X$ is contained in a compact neighborhood.