Regular space

From Topospaces
Revision as of 09:44, 20 August 2007 by Vipul (talk | contribs)

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


This article is about a basic definition in topology.
VIEW: Definitions built on this | Facts about this | Survey articles about this
View a complete list of basic definitions in topology

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

Weaker properties