Locally Hausdorff space

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 Hausdorffness. View other variations of Hausdorffness

Definition

Symbol-free definition

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

• Every point has an open neighbourhood which is Hausdorff
• Given any point, and any open neighbourhood of the point, there is a smaller open neighbourhood of the point which is Hausdorff.

Relation with other properties

Stronger properties

• Hausdorff space
• Locally metrizable space
• Locally Euclidean space

Weaker properties

• T1 space