Theorems · Theorem · functional analysis
isOpenMap_barycentric_coord
∀ {ι : Type u_1} {𝕜 : Type u_2} {E : Type u_3} {P : Type u_4} [inst : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜]
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] [inst_4 : MetricSpace P] [inst_5 : NormedAddTorsor E P]
[Nontrivial ι] (b : AffineBasis ι 𝕜 P) (i : ι), IsOpenMap ⇑(b.coord i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- Nontrivialstatement and proof · cited by 2,416
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineMapstatement · cited by 674
- IsOpenMapstatement · cited by 253
- AffineMap.linearproof · cited by 105
- AffineBasisstatement and proof · cited by 65
Cited by1
Results whose statement or proof uses this declaration.
- AffineBasis.interior_convexHullproof · cited by 1