Normal space
This is an old revision of this page, as edited by Jaques (talk | contribs) at 02:17, April 7, 2007. It may differ significantly from current revision.
Normal space (or T4 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.