# Polish space

A Polish space^{} is a topological space^{} that is homeomorphic^{} to some complete^{} separable metric space.

Equivalently, a topological space is a Polish space if it is separable and completely metrizable.

Examples of Polish spaces are the euclidean space ${\mathbb{R}}^{n}$ (with the usual topology), the Cantor space, and the Baire space^{} (http://planetmath.org/BaireSpace2).

Title | Polish space |
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Canonical name | PolishSpace |

Date of creation | 2013-03-22 14:59:18 |

Last modified on | 2013-03-22 14:59:18 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 5 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 54E50 |

Related topic | TopologicalGSpace |

Related topic | PolishGroup |

Related topic | CategoryOfPolishGroups |

Related topic | SpacesHomeomorphicToBaireSpace |