T3 space


A regular spaceMathworldPlanetmathPlanetmath is a topological spaceMathworldPlanetmath in which points and closed sets can be separated by open sets; in other words, given a closed set A and a point xA, there are disjoint open sets U and V such that xU and AV.

A T3 space is a regularPlanetmathPlanetmath T0-space (http://planetmath.org/T0Space). A T3 space is necessarily also T2, that is, HausdorffPlanetmathPlanetmath.

Note that some authors make the opposite distinction between T3 spaces and regular spaces, that is, they define T3 spaces to be topological spaces in which points and closed sets can be separated by open sets, and then define regular spaces to be topological spaces that are both T3 and T0. (With these definitions, T3 does not imply T2.)

Title T3 space
Canonical name T3Space
Date of creation 2013-03-22 12:18:24
Last modified on 2013-03-22 12:18:24
Owner yark (2760)
Last modified by yark (2760)
Numerical id 14
Author yark (2760)
Entry type Definition
Classification msc 54D10
Related topic TychonoffPlanetmathPlanetmath
Related topic T2Space
Related topic T1Space
Related topic T0Space
Defines T3
Defines regular
Defines regular space