# Definition:Strongly Locally Compact Space

## Definition

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

### Definition 1

The space $T$ is strongly locally compact if and only if:

every point of $S$ is contained in an open set whose closure is compact.

### Definition 2

The space $T$ is strongly locally compact if and only if:

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 defined as

Some sources define a strongly locally compact space as what on $\mathsf{Pr} \infty \mathsf{fWiki}$ is called a locally compact space.

## Also see

• Results about strongly locally compact spaces can be found here.