A topological spaceMathworldPlanetmath X is said to be normal if X is T1 (i.e. singletons are closed), and for all disjoint closed sets D,FX there exist disjoint open sets U and V such that CU and DV (i.e, X is also T4).

Some authors do not require the T1 axiom as part of this definition.

Title normal
Canonical name Normal
Date of creation 2013-03-22 12:12:39
Last modified on 2013-03-22 12:12:39
Owner Koro (127)
Last modified by Koro (127)
Numerical id 14
Author Koro (127)
Entry type Definition
Classification msc 54D15
Synonym normalityPlanetmathPlanetmath
Synonym normal
Related topic SeparationAxioms
Related topic TychonoffPlanetmathPlanetmath
Related topic HausdorffPlanetmathPlanetmath
Related topic CompletelyNormal
Related topic T2Space
Related topic AConnectedNormalSpaceWithMoreThanOnePointIsUncountable2
Related topic AConnectedNormalSpaceWithMoreThanOnePointIsUncountable
Related topic ApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces