partition of unity

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partition of unity [pär′tish·ən əv ′yü·nəd·ē]

(mathematics)

On a topological spaceX,this is a covering by open setsU_αwith continuous functions ƒ_αfromXto [0,1], where each ƒ_αis zero on all but a finite number of theU_α, and the sum of all these ƒ_αat any point equals 1.

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