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Partition of unity

Set of functions from a topological space to [0,1] which sum to 1 for any input

In mathematics, a partition of unity on 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 zero, and the sum of all the function values at ⁠⁠ is 1, i.e.,

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