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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>.
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]]