Locally compact Hausdorff space

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

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

• Compact Hausdorff space
• Manifold

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