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T0 space (Definition)

A topological space $(X,\tau)$ is said to be $T_0$ (or said to hold the $T_0$ axiom ) if, given $x,y\in X$, ($x\neq y$), there exists an open set $U\in\tau$ such that ($x\in U$ and $y\notin U$) or ($x\notin U$ and $y\in U$)

An example of $T_0$ space is the Sierpinski space, which is not $T_1$.



"T0 space" is owned by drini. [ owner history (1) ]
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See Also: ball, T1 space, Hausdorff space, regular space, T3 space

Other names:  T0
Keywords:  Topology
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Cross-references: Sierpinski space, open set, axiom, topological space
There are 10 references to this entry.

This is version 8 of T0 space, born on 2002-02-08, modified 2002-02-09.
Object id is 1850, canonical name is T0Space.
Accessed 4082 times total.

Classification:
AMS MSC: 54D10 (General topology :: Fairly general properties :: Lower separation axioms )
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