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 seperated by a [[continuous function]]. | 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 seperated 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:Topology]] | [[Category:Topology]] | ||
Revision as of 18:31, April 6, 2007
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 seperated 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.
