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Theorems · Theorem · general topology

PartitionOfUnity.sum_nonneg

∀ {ι : Type u} {X : Type v} [inst : TopologicalSpace X] {s : Set X} (f : PartitionOfUnity ι X s) (x : X),
  0 ≤ ∑ᶠ (i : ι), (f i) x
Defined in
Mathlib.Topology.PartitionOfUnity
Cited by
1 results in Mathlib
Foundations
Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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SmoothPartitionOfUnity.sum_nonneg · cited by 1SmoothPartitionOfUnity.su…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealTopologicalSpace · cited by 24529TopologicalSpaceContinuousMap · cited by 2491ContinuousMapfinsum · cited by 286finsumPartitionOfUnity · cited by 47PartitionOfUnityPartitionOfUnity.nonneg · cited by 5PartitionOfUnity.nonnegfinsum_nonneg · cited by 4finsum_nonnegPartitionOfUnity.sum_nonnegCITED BYCITES

Cites9

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Cited by1

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