PlanetMath: existence of partitions of unity

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existence of partitions of unity

(Theorem)

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 $\{U_i\}_{i \in J}$ .

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Cross-references: partition of unity, covering, open, Hausdorff space, paracompact, theorem
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This is version 2 of existence of partitions of unity, born on 2007-07-18, modified 2007-07-18.
Object id is 9780, canonical name is ExistenceOfPartitionsOfUnity.
Accessed 975 times total.

Classification:

54D20 (General topology :: Fairly general properties :: Noncompact covering properties )

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