Difference between revisions of "Regular space"
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| − | + | A '''regular space''' is a Hausdorff [[topological space]] in which, given any closed set F and any point x that does not belong to F, there exist an open set U of x and an open set V of F that are disjoint. A space which is both regular and T<sub>1</sub> is called T<sub>3</sub>. | |
| − | [[Category: | + | |
| + | The subspace of a regular space is a regular space; the product of 2 regular spaces is a regular space. | ||
| + | [[Category:Topology]] | ||
Latest revision as of 18:20, July 13, 2016
A regular space is a Hausdorff topological space in which, given any closed set F and any point x that does not belong to F, there exist an open set U of x and an open set V of F that are disjoint. A space which is both regular and T1 is called T3.
The subspace of a regular space is a regular space; the product of 2 regular spaces is a regular space.