# Locally compact Hausdorff space

From Topospaces

*This article describes a property of topological spaces obtained as a conjunction of the following two properties:* locally compact space and Hausdorff space

## Contents

## Definition

A topological space is termed **locally compact Hausdorff** if it satisfies the following equivalent conditions:

- It is locally compact and Hausdorff
- It is strongly locally compact and Hausdorff
- It has a one-point compactification

## Relation with other properties

### Stronger properties

### Weaker properties

- Completely regular space:
*For full proof, refer: locally compact Hausdorff implies completely regular* - Locally normal space
- Baire space:
*For full proof, refer: Locally compact Hausdorff implies Baire* - Locally compact space
- Strongly locally compact space