Editing Normal space (section)

{{Short description|Type of topological space}}
{{for|normal vector space|normal (geometry)}}
{{Separation axioms}}

In [[topology]] and related branches of [[mathematics]], a '''normal space''' is a [[topological space]] in which any two disjoint [[closed set]]s have disjoint [[open neighborhood]]s.  Such spaces need not be [[Hausdorff space|Hausdorff]] in general.  A normal Hausdorff space is called a '''T<sub>4</sub> space'''.  Strengthenings of these concepts are detailed in the article below and include '''completely normal spaces''' and '''perfectly normal spaces''', and their Hausdorff variants: '''T<sub>5</sub> spaces''' and '''T<sub>6</sub> spaces'''.
All these conditions are examples of [[separation axiom]]s.