Locally normal 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 normality. View other variations of normality

Definition

A topological space is termed locally normal if every point in it has an open neighbourhood which is normal.

Relation with other properties

Stronger properties

• Locally metrizable space
• Normal space: For proof of the implication, refer normal implies locally normal and for proof of its strictness (i.e. the reverse implication being false) refer locally normal not implies normal

Weaker properties

• Locally Hausdorff space

Facts

There exist locally normal completely regular spaces that are not normal. The classical example is the Moore plane.