# Definition:Strongly Locally Compact Space

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## Definition

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

### Definition 1

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

### 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

- Strongly Locally Compact Space may not be Locally Compact
- Locally Compact Space may not be Strongly Locally Compact
- Sequence of Implications of Local Compactness Properties

- Results about
**strongly locally compact spaces**can be found here.