Theorems · Definition · field theory
Submonoid.unitSphere
(𝕜 : Type u_2) → [inst : SeminormedRing 𝕜] → [NormMulClass 𝕜] → [NormOneClass 𝕜] → Submonoid 𝕜
Unit sphere in a seminormed ring (with strictly multiplicative norm) as a bundled
Submonoid.
- Defined in
- Mathlib.Analysis.Normed.Field.UnitBall
- Cited by
- 85 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- SeminormedRingstatement and proof · cited by 446
- Metric.sphereproof · cited by 371
- NormOneClassstatement and proof · cited by 136
- NormMulClassstatement and proof · cited by 66
Cited by87
Results whose statement or proof uses this declaration.
- Circleproof · cited by 227
- Circle.coe_expstatement · cited by 10
- Circle.extstatement · cited by 8
- fourier_applystatement · cited by 7
- Circle.exp_argstatement · cited by 6
- Circle.coe_ne_zerostatement · cited by 5
- Circle.norm_coestatement · cited by 5
- Circle.coe_pathstatement · cited by 4
- Real.hasDerivAt_fourierCharstatement · cited by 4
- Circle.arg_expstatement · cited by 3
- Real.Angle.coe_toCirclestatement · cited by 3
- Circle.path_image_Ioc_of_nestatement · cited by 3