Theorems · Theorem · general topology
BumpCovering.toPOUFun_zero_of_zero
∀ {ι : Type u} {X : Type v} [inst : TopologicalSpace X] {s : Set X} (f : BumpCovering ι X s) {i : ι} {x : X},
(f i) x = 0 → f.toPOUFun i x = 0- Defined in
- Mathlib.Topology.PartitionOfUnity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousMapstatement · cited by 2,491
- MulZeroClass.zero_mulproof · cited by 1,625
- finprodproof · cited by 257
- BumpCoveringstatement and proof · cited by 46
- WellOrderingRelproof · cited by 30
- BumpCovering.toPOUFunstatement · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- BumpCovering.support_toPOUFun_subsetproof · cited by 2
- BumpCovering.toPartitionOfUnity_zero_of_zeroproof · cited by 1