Theorems · Theorem · general topology
BumpCovering.support_toPOUFun_subset
∀ {ι : Type u} {X : Type v} [inst : TopologicalSpace X] {s : Set X} (f : BumpCovering ι X s) (i : ι),
Function.support (f.toPOUFun i) ⊆ Function.support ⇑(f i)- Defined in
- Mathlib.Topology.PartitionOfUnity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousMapstatement · cited by 2,491
- Function.supportstatement · cited by 610
- BumpCoveringstatement and proof · cited by 46
- BumpCovering.toPOUFunstatement · cited by 6
- BumpCovering.toPOUFun_zero_of_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- BumpCovering.support_toPartitionOfUnity_subsetproof · cited by 3
- BumpCovering.sum_toPOUFun_eqproof · cited by 1