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T3 space∗ yark† 2013-03-21 13:26:36 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. 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 .) ∗ hT3Spacei created: h2013-03-21i by: hyarki version: h31866i Privacy setting: h1i hDefinitioni h54D10i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1
