# strongly paracompact space

A collection^{} $\mathcal{A}$ of sets is said to be *star-finite*
if each member of $\mathcal{A}$
meets only finitely many members of $\mathcal{A}$.

A topological space^{} $X$ is said to be *strongly paracompact*
if every open cover of $X$ has a star-finite open refinement.

A star-finite open cover of a topological space
is clearly locally finite^{}.
Therefore, every strongly paracompact space is paracompact
(as the name suggests).

Title | strongly paracompact space |
---|---|

Canonical name | StronglyParacompactSpace |

Date of creation | 2013-03-22 17:09:01 |

Last modified on | 2013-03-22 17:09:01 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 5 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 54D20 |

Synonym | strongly paracompact topological space |

Defines | strongly paracompact |

Defines | star-finite |

Defines | star finite |