Difference between revisions of "Completely regular space"
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| − | A [[topological space]] X is completely regular if singleton sets are closed in X and any point x in X and any closed subset B of X not containing x can be | + | A [[topological space]] X is a '''completely regular space''' (or '''T<sub>3½</sub> space''') if singleton sets are closed in X and any point x in X and any closed subset B of X not containing x can be separated by a [[continuous function]]. |
| − | The subspace of a completely regular space is a completely regular space; the product of 2 completely regular spaces is a completely regular space. | + | The subspace of a completely regular space is a completely regular space; the product of 2 completely regular spaces is a completely regular space. Every subspace of a [[normal space]] is a completely regular space. |
| − | [[Category: | + | [[Category:Topology]] |
Latest revision as of 23:39, June 28, 2009
A topological space X is a completely regular space (or T3½ space) if singleton sets are closed in X and any point x in X and any closed subset B of X not containing x can be separated by a continuous function.
The subspace of a completely regular space is a completely regular space; the product of 2 completely regular spaces is a completely regular space. Every subspace of a normal space is a completely regular space.
