# residual

A subspace^{} $A$ of a topological space^{} $X$ is called residual (or comeager) if and only if it is second category and its complement $X\setminus A$ is first category. Equivalently, a set is residual if and only if it contains a countable^{} intersection^{} of open (http://planetmath.org/OpenSet) dense sets.

Title | residual |
---|---|

Canonical name | Residual |

Date of creation | 2013-03-22 13:04:05 |

Last modified on | 2013-03-22 13:04:05 |

Owner | mps (409) |

Last modified by | mps (409) |

Numerical id | 7 |

Author | mps (409) |

Entry type | Definition |

Classification | msc 54E52 |

Related topic | BaireCategoryTheorem |

Related topic | SardsTheorem |

Defines | comeager |