# existence of partitions of unity

Theorem - Let $X$ be a paracompact Hausdorff space and ${\{{U}_{i}\}}_{i\in J}$ an open covering of $X$. Then there exists a partition of unity^{} on $X$ subordinate to ${\{{U}_{i}\}}_{i\in J}$.

Title | existence of partitions of unity |
---|---|

Canonical name | ExistenceOfPartitionsOfUnity |

Date of creation | 2013-03-22 17:24:29 |

Last modified on | 2013-03-22 17:24:29 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 5 |

Author | asteroid (17536) |

Entry type | Theorem |

Classification | msc 54D20 |