# Regular Hausdorff space

From Topospaces

## Contents

## Definition

A topological space is termed a **regular Hausdorff space** or a space if it satisfies the following equivalent conditions:

- It is both a regular space and a Hausdorff space.
- It is both a regular space and a T1 space.
- It is both a regular space and a Kolmogorov space (i.e., a space).

Note that outside of point-set topology, and in many elementary treatments, the term *regular space* is used to stand for regular 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

*In the T family (properties of topological spaces related to separation axioms), this is called:* T3

## Relation with other properties

### Stronger properties

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

regular space | |FULL LIST, MORE INFO | |||

Hausdorff space | Urysohn space|FULL LIST, MORE INFO | |||

T1 space | Hausdorff space, Urysohn space|FULL LIST, MORE INFO | |||

Kolmogorov space | Hausdorff space, Urysohn space|FULL LIST, MORE INFO |