# normal

A topological space $X$ is said to be normal if $X$ is $T_{1}$ (i.e. singletons are closed), and for all disjoint closed sets $D,F\subseteq X$ there exist disjoint open sets $U$ and $V$ such that $C\subseteq U$ and $D\subseteq V$ (i.e, $X$ is also $T_{4}$).

Some authors do not require the $T_{1}$ 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 normality Synonym normal Related topic SeparationAxioms Related topic Tychonoff Related topic Hausdorff Related topic CompletelyNormal Related topic T2Space Related topic AConnectedNormalSpaceWithMoreThanOnePointIsUncountable2 Related topic AConnectedNormalSpaceWithMoreThanOnePointIsUncountable Related topic ApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces