T3 space
A regular space is a topological space
in which points and closed sets can be separated by open sets;
in other words, given a closed set A and a point x∉A,
there are disjoint open sets U and V such that x∈U and A⊆V.
A T3 space is a regular T0-space (http://planetmath.org/T0Space).
A T3 space is necessarily also T2, that is, Hausdorff
.
Note that some authors make the opposite distinction between T3 spaces and regular spaces, that is, they define T3 spaces to be topological spaces in which points and closed sets can be separated by open sets, and then define regular spaces to be topological spaces that are both T3 and T0. (With these definitions, T3 does not imply T2.)
Title | T3 space |
Canonical name | T3Space |
Date of creation | 2013-03-22 12:18:24 |
Last modified on | 2013-03-22 12:18:24 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 14 |
Author | yark (2760) |
Entry type | Definition |
Classification | msc 54D10 |
Related topic | Tychonoff |
Related topic | T2Space |
Related topic | T1Space |
Related topic | T0Space |
Defines | T3 |
Defines | regular |
Defines | regular space |