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Partition Of Unity

  • Definition: Let {U_1, ... , U_n} be a finite indexed open covering of the space X. An indexed family of continuous functions f_i: X -> [0, 1] for i=1, ... , n, is said to be a partition of unity dominated by {U_i} if: (1) (support f_i) is a subset of U_i for each i. (2) the sum of f_i(x) as i goes from 1 to n equals 1 for each x.

    Source: Topology (second edition) by James R. Munkres

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