Definition:Strongly Locally Compact Space/Definition 2

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

The space $T$ is strongly locally compact :
 * every point has a closed compact neighborhood.

That is:
 * every point of $S$ is contained in an open set which is contained in a closed compact subspace.

Also see

 * Equivalence of Definitions of Strongly Locally Compact Space