6,068
edits
Changes
Jump to navigation
Jump to search
mLine 1:
Line 1: − +
no edit summary
Normal space is a Hausdorff [[topological space]] in which, given any pair of disjoint closed sets E and F, there exist neighbourhoods U of E and V of F that are disjoint. A product of normal spaces is not necessarily normal, the [[Sorgenfrey plane]] is an example of a product of normal spaces that is not normal. On the other hand, every regular space with a countable basis is normal. Every subspace of a normal space is a [[completely regular space]].
'''Normal space''' (or '''T<sub>4</sub> space''') is a Hausdorff [[topological space]] in which, given any pair of disjoint closed sets E and F, there exist neighbourhoods U of E and V of F that are disjoint. A product of normal spaces is not necessarily normal, the [[Sorgenfrey plane]] is an example of a product of normal spaces that is not normal. On the other hand, every regular space with a countable basis is normal. Every subspace of a normal space is a [[completely regular space]].
By the [[Urysohn lemma]], any 2 disjoint, closed subsets of a normal space can be seperated by a [[continuous function]]. The converse also hold.
By the [[Urysohn lemma]], any 2 disjoint, closed subsets of a normal space can be seperated by a [[continuous function]]. The converse also hold.
[[category: Topology]]
[[category: Topology]]