# 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 ExistenceOfPartitionsOfUnity 2013-03-22 17:24:29 2013-03-22 17:24:29 asteroid (17536) asteroid (17536) 5 asteroid (17536) Theorem msc 54D20