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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
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