Theorems · Definition · field theory
unitSphereToUnits
(𝕜 : Type u_2) → [inst : NormedDivisionRing 𝕜] → ↑(Metric.sphere 0 1) →* 𝕜ˣ
Monoid homomorphism from the unit sphere in a normed division ring to the group of units.
- Defined in
- Mathlib.Analysis.Normed.Field.UnitBall
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
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.
- Realstatement · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- Metric.spherestatement and proof · cited by 371
- NormedDivisionRingstatement and proof · cited by 360
- Units.mk0proof · cited by 181
- Submonoid.unitSphereproof · cited by 85
- Submonoid.subtypeproof · cited by 26
- Units.liftRightproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Circle.toUnitsproof · cited by 1
- unitSphereToUnits_apply_coestatement · cited by 0
- unitSphereToUnits_injectivestatement and proof · cited by 0