Regular space

This article defines a property of topological space that is pivotal (viz important) among currently studied properties of topological spaces

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

This article is about a basic definition in topology.
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Definition

Symbol-free definition

A topological space is said to be reguilar if it satisfies the following two conditions:

• It is a T1 space viz all points are closed
• Given a point and a closed set not containing it, there are disjoint open sets containing the point and the closed set respectively.

Relation with other properties

Stronger properties

• Normal space
• Completely regular space

Weaker properties

• Hausdorff space
• T1 space
• T0 space