T4 space

Definition 1.

[1] Suppose X is a topological spaceMathworldPlanetmath. Further, suppose that for any two disjoint closed setsPlanetmathPlanetmath A,BX, there are two disjoint open sets U and V such that AU and BV. Then we say that X is a T4 space.


It should be pointed out that there is no standard convention for separation axiomsMathworldPlanetmathPlanetmath in topology. The above definition follows [1]. However, in some references (e.g. [2]) the meaning of T4 and normal are exchanged.


  • 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
  • 2 J.L. Kelley, General Topology, D. van Nostrand Company, Inc., 1955.
Title T4 space
Canonical name T4Space
Date of creation 2013-03-22 14:42:15
Last modified on 2013-03-22 14:42:15
Owner matte (1858)
Last modified by matte (1858)
Numerical id 5
Author matte (1858)
Entry type Definition
Classification msc 54D15
Related topic SeparationAxioms
Related topic HowIsNormalityAndT4DefinedInBooks