Partition of unity
Set of functions from a topological space to [0,1] which sum to 1 for any input / From Wikipedia, the free encyclopedia
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In mathematics, a partition of unity of a topological space is a set of continuous functions from to the unit interval [0,1] such that for every point :
- there is a neighbourhood of where all but a finite number of the functions of are 0, and
- the sum of all the function values at is 1, i.e.,
Partitions of unity are useful because they often allow one to extend local constructions to the whole space. They are also important in the interpolation of data, in signal processing, and the theory of spline functions.