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Partition of unity
In mathematics, a partition of unity of a topological space X is a set of continuous functions {ρi} from X to the unit interval [0,1] such that every point has a neighbourhood where all but a finite number of the functions are identically zero, and the sum of all the functions on the entire space is identically 1,
Partitions of unity are useful because they often allow one to extend local constructions to the whole space.
See also: paracompact space
Last updated: 10-18-2005 12:35:06
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details