# T0 space

A topological space $(X,\tau)$ is said to be $T_{0}$ (or to satisfy the $T_{0}$ axiom ) if for all distinct $x,y\in X$ there exists an open set $U\in\tau$ such that either $x\in U$ and $y\notin U$ or $x\notin U$ and $y\in U$.

All $T_{1}$ spaces (http://planetmath.org/T1Space) are $T_{0}$. An example of $T_{0}$ space that is not $T_{1}$ 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