# first axiom of countability

A topological space^{} $(X,\tau )$ satisfies the first axiom of countability^{}
if the neighborhood system of every point $x\in X$ has a countable local base. A space that satisfies the first axiom of countability is said to be *first-countable*.

Title | first axiom of countability |
---|---|

Canonical name | FirstAxiomOfCountability |

Date of creation | 2013-03-22 12:22:13 |

Last modified on | 2013-03-22 12:22:13 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 5 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 54-00 |

Synonym | first-countable |

Related topic | SecondCountable |

Related topic | LocalBase |