Block, SkipCaptcha, Automoderated users, Bots, edit
57,719
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − + − + − +
→top: clean up & uniformity
'''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]].
A '''Normal space''' is a [[Hausdorff 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]]. A normal space which is also T<sub>1</sub> is called T<sub>4</sub>.
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 separated by a [[continuous function]]. The converse also hold.
[[category: Topology]]
[[Category:Topology]]