# point-finite

A collection^{} $\mathcal{U}$ of subsets of a topological space^{} $X$ is said to be *point-finite* if every point of $X$ lies in only finitely many members of $\mathcal{U}$.

Compare this to the stronger property of being locally finite^{}.

Point-finiteness is used in the definition of metacompactness.

Title | point-finite |

Canonical name | Pointfinite |

Date of creation | 2013-03-22 16:17:02 |

Last modified on | 2013-03-22 16:17:02 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 5 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 54A99 |

Synonym | point finite |

Related topic | LocallyFinite |

Related topic | Metacompact |

Defines | point finite collection |

Defines | point-finite collection |

Defines | point finiteness |

Defines | point-finiteness |