partition of unity
set of continuous functions from a topological space to the unit interval [0,1] such that for every point x, there is a neighborhood of x where a cofinite number of the functions are 0, and such that the sum of all the function values at x is 1
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partition of unity
Summary
partition of unity ranks in the top 2% of general entities by monthly Wikipedia readership (150 views/month).[1]
Key Facts
- partition of unity's image is recorded as Partition of unity illustration.svg[2].
- partition of unity's subclass of is recorded as set[3].
- partition of unity's Freebase ID is recorded as /m/0c_sh[4].
- partition of unity's defining formula is recorded as \begin{aligned}&F\subset\mathcal C^0(X,\mathbb R)\&\forall x\in X\exists U\in\operatorname{Open}(X)\colon(x\in U\land{f\restriction U\ne 0}<\aleph_0)\&\forall x\in X\colon\sum_{f\in F}f(x)=1\end{aligned}<sup id="cite-C4" class="cite-ref" title="partition of unity — defining formula (P2534): \begin{aligned}&F\subset\mathcal C^0(X,\mathbb R)\&\forall x\in X\exists U\in\operatorname{Open}(X)\colon(x\in U\land{f\restriction U\ne 0}<\aleph_0)\">[5].
- partition of unity's MathWorld ID is recorded as PartitionofUnity[6].
- partition of unity's nLab ID is recorded as partition of unity[7].
- partition of unity's maintained by WikiProject is recorded as WikiProject Mathematics[8].
- partition of unity's Microsoft Academic ID is recorded as 102205669[9].
- partition of unity's ProofWiki ID is recorded as Definition:Partition_of_Unity_(Topology)[10].
- partition of unity's in defining formula is recorded as X[11].
- partition of unity's in defining formula is recorded as F[12].
- partition of unity's in defining formula is recorded as f[13].
- partition of unity's in defining formula is recorded as \operatorname{Open}(X)[14].
- partition of unity's in defining formula is recorded as U[15].
- partition of unity's in defining formula is recorded as \aleph_0[16].
- partition of unity's in defining formula is recorded as 1[17].
- partition of unity's OpenAlex ID is recorded as C102205669[18].
Why It Matters
partition of unity ranks in the top 2% of general entities by monthly Wikipedia readership (150 views/month).[1] It has Wikipedia articles in 14 language editions, a strong signal of global cultural recognition.[19]