# equivalent statement of Baire category theorem

Let $(X,d)$ be a complete metric space. Then every subset
$B\subset X$ of first category has empty interior.

Corollary: Every non empty complete metric space is of second category.

Title | equivalent statement of Baire category theorem |
---|---|

Canonical name | EquivalentStatementOfBaireCategoryTheorem |

Date of creation | 2013-03-22 14:04:49 |

Last modified on | 2013-03-22 14:04:49 |

Owner | gumau (3545) |

Last modified by | gumau (3545) |

Numerical id | 8 |

Author | gumau (3545) |

Entry type | Theorem |

Classification | msc 54E52 |