# Strongly locally compact space

From Topospaces

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

This is a variation of compactness. View other variations of compactness

## Definition

A topological space is termed **strongly locally compact** if, given any point, and any open neighbourhood of the point, there exists a smaller open neighbourhood, whose closure is compact, and such that the closure lies completely inside the bigger open neighbourhood.

Note that for a T1 space, strongly locally compact is the same thing as a locally compact Hausdorff space.