Theorems · Definition · general topology
BumpCovering.toFun
{ι : Type u_1} →
{X : Type u_2} → [inst : TopologicalSpace X] → {s : optParam (Set X) Set.univ} → BumpCovering ι X s → ι → C(X, ℝ)The collections of continuous functions underlying this bump covering
- Defined in
- Mathlib.Topology.PartitionOfUnity
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 114 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement and proof · cited by 3,945
- ContinuousMapstatement · cited by 2,491
- BumpCoveringstatement and proof · cited by 46
Cited by5
Results whose statement or proof uses this declaration.
- BumpCovering.eventuallyEq_one'statement · cited by 1
- BumpCovering.le_one'statement · cited by 1
- BumpCovering.locallyFinite'statement · cited by 1
- BumpCovering.nonneg'statement · cited by 1
- BumpCovering.toFun_eq_coestatement · cited by 0