# locally finite collection

Let $\mathcal{C}$ be a collection^{} of subsets of a topological space^{} $X$.

$\mathcal{C}$ is said to be *locally finite ^{}*
if for all $x\in X$ there is a neighbourhood $U$ of $x$
such that $U\cap A=\mathrm{\varnothing}$ for all but finitely many $A\in \mathcal{C}$.

Similarly, $\mathcal{C}$ is said to be *locally countable*
if for all $x\in X$ there is a neighbourhood $U$ of $x$
such that $U\cap A=\mathrm{\varnothing}$ for all but countably many $A\in \mathcal{C}$.

Title | locally finite collection |
---|---|

Canonical name | LocallyFiniteCollection |

Date of creation | 2013-03-22 12:12:51 |

Last modified on | 2013-03-22 12:12:51 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 11 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 54D20 |

Related topic | PointFinite |

Defines | locally finite |

Defines | locally countable collection |

Defines | locally countable |