# completely metrizable

Let $X$ be a topological space^{}. $X$ is said to be *completely metrizable* if there is a metric $d$ on $X$ under which $X$ is complete^{}.

In particular, a completely metrizable space is metrizable.

completely metrizable

Title | completely metrizable |
---|---|

Canonical name | CompletelyMetrizable |

Date of creation | 2013-03-22 12:13:56 |

Last modified on | 2013-03-22 12:13:56 |

Owner | Evandar (27) |

Last modified by | Evandar (27) |

Numerical id | 5 |

Author | Evandar (27) |

Entry type | Definition |

Classification | msc 54E35 |

Synonym | complete metrizability |

Synonym | topologically complete |

Synonym | topological completeness |