Difference between revisions of "Regular space"
Jump to navigation
Jump to search
m |
|||
| Line 1: | Line 1: | ||
| − | 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. | + | '''Regular space''' (or '''T<sub>3</sub> spaces''') 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. |
The subspace of a regular space is a regular space; the product of 2 regular spaces is a regular space. | The subspace of a regular space is a regular space; the product of 2 regular spaces is a regular space. | ||
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 02:14, April 7, 2007
Regular space (or T3 spaces) 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.
The subspace of a regular space is a regular space; the product of 2 regular spaces is a regular space.