Locally compact 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

Stronger properties

 * Compact Hausdorff space
 * Manifold

Weaker properties

 * Completely regular space:
 * Locally normal space
 * Baire space:
 * Locally compact space
 * Strongly locally compact space