# Baire space is universal for Polish spaces

The following result says that Baire space^{}, $\mathcal{N}$, is *universal ^{}* for Polish spaces

^{}.

###### Theorem.

Let $X$ be a nonempty Polish space. Then, there is a continuous^{} and onto map $f\mathrm{:}\mathrm{N}\mathrm{\to}X$.

Title | Baire space is universal for Polish spaces |
---|---|

Canonical name | BaireSpaceIsUniversalForPolishSpaces |

Date of creation | 2013-03-22 18:46:54 |

Last modified on | 2013-03-22 18:46:54 |

Owner | gel (22282) |

Last modified by | gel (22282) |

Numerical id | 5 |

Author | gel (22282) |

Entry type | Theorem |

Classification | msc 54E50 |

Related topic | PolishSpace |

Related topic | InjectiveImagesOfBaireSpace |