# Locally normal space

From Topospaces

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

## Contents

## 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

## Facts

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