Difference between revisions of "Normal space"

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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.
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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.
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]

Revision as of 21:59, March 22, 2007

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.