Regular space

Separation axioms
in topological spaces
Kolmogorov classification
T0 (Kolmogorov)
T1 (Fréchet)
T2 (Hausdorff)
T2½(Urysohn)
completely T2 (completely Hausdorff)
T3 (regular Hausdorff)
T(Tychonoff)
T4 (normal Hausdorff)
T5 (completely normal
 Hausdorff)
T6 (perfectly normal
 Hausdorff)

In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained in C have non-overlapping open neighborhoods.[1] Thus p and C can be separated by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "a regular Hausdorff space". These conditions are examples of separation axioms.

  1. ^ Munkres, James R. (2000). Topology (2nd ed.). Prentice Hall. ISBN 0-13-181629-2.