Topology | Differential topology

Partition of unity

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. (Wikipedia).

Partition of unity
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Related pages

Topological space | Mollifier | Signal processing | Support (mathematics) | Gluing axiom | Finite set | Sobolev space | Interpolation | Unit interval | Bernstein polynomial | Linkwitz–Riley filter | Neighbourhood (mathematics) | Mathematics | Set (mathematics) | Method of steepest descent | Cartesian product | Category (mathematics) | Analytic manifold | Compact space | Analytic continuation | Bump function | Paracompact space | Volume form