# 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 |