T0 space

A topological spaceMathworldPlanetmath (X,τ) is said to be T0 (or to satisfy the T0 axiom ) if for all distinct x,yX there exists an open set Uτ such that either xU and yU or xU and yU.

All T1 spaces (http://planetmath.org/T1Space) are T0. An example of T0 space that is not T1 is the 2-point Sierpinski space.

Title T0 space
Canonical name T0Space
Date of creation 2013-03-22 12:18:12
Last modified on 2013-03-22 12:18:12
Owner yark (2760)
Last modified by yark (2760)
Numerical id 13
Author yark (2760)
Entry type Definition
Classification msc 54D10
Synonym Kolmogorov space
Synonym Kolmogoroff space
Related topic Ball
Related topic T1Space
Related topic T2Space
Related topic RegularSpace
Related topic T3Space
Defines T0