Theorems · Theorem · functional analysis
ContinuousLinearEquiv.lipschitz
∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_4} {F : Type u_5} [inst : NontriviallyNormedField 𝕜]
[inst_1 : NontriviallyNormedField 𝕜₂] [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup F]
[inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ₁₂]
{σ₂₁ : 𝕜₂ →+* 𝕜} [inst_7 : RingHomInvPair σ₁₂ σ₂₁] [inst_8 : RingHomInvPair σ₂₁ σ₁₂] (e : E ≃SL[σ₁₂] F),
LipschitzWith ‖↑e‖₊ ⇑e- Defined in
- Mathlib.Analysis.Normed.Operator.NNNorm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NormedSpacestatement and proof · cited by 12,499
- RingHomstatement and proof · cited by 10,189
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement · cited by 952
- ContinuousLinearEquivstatement and proof · cited by 743
- RingHomInvPairstatement and proof · cited by 523
- ContinuousLinearEquiv.toContinuousLinearMapstatement and proof · cited by 448
- LipschitzWithstatement · cited by 316
- RingHomIsometricstatement and proof · cited by 282
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousLinearEquiv.antilipschitzproof · cited by 8
- LocallyBoundedVariationOn.ae_differentiableWithinAt_of_memproof · cited by 4
- LipschitzOnWith.ae_differentiableWithinAt_of_memproof · cited by 2
- ContinuousLinearEquiv.dimH_imageproof · cited by 2
- LipschitzOnWith.extend_finite_dimensionproof · cited by 1