# metrizable

A topological space^{} $(X,\mathcal{T})$ is said to be *metrizable* if there is a metric $d:X\to [0,\mathrm{\infty})$ such that the topology induced by $d$ is $\mathcal{T}$.

Title | metrizable |

Canonical name | Metrizable |

Date of creation | 2013-03-22 12:12:44 |

Last modified on | 2013-03-22 12:12:44 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 6 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 54-00 |

Classification | msc 55-00 |

Classification | msc 22-00 |

Synonym | metrization |

Synonym | metrizable space |

Related topic | Metric |

Related topic | UrysohnMetrizationTheorem |

Related topic | CategoryOfPolishGroups |