Theorems · Theorem · general topology
AddMonoidHomClass.antilipschitz_of_bound
∀ {𝓕 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : SeminormedAddGroup E] [inst_1 : SeminormedAddGroup F]
[inst_2 : FunLike 𝓕 E F] [AddMonoidHomClass 𝓕 E F] (f : 𝓕) {K : NNReal},
(∀ (x : E), ‖x‖ ≤ ↑K * ‖f x‖) → AntilipschitzWith K ⇑f- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 152 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 and proof · cited by 62,936
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- FunLikestatement and proof · cited by 2,560
- NNReal.toRealstatement and proof · cited by 1,260
- map_addproof · cited by 964
- map_negproof · cited by 378
- SeminormedAddGroupstatement and proof · cited by 331
- AddMonoidHomClassstatement and proof · cited by 252
- AntilipschitzWithstatement · cited by 132
- dist_eq_norm_neg_addproof · cited by 46
Cited by7
Results whose statement or proof uses this declaration.
- Complex.antilipschitz_equivRealProdproof · cited by 2
- Unitization.antilipschitzWith_addEquivproof · cited by 2
- ContinuousLinearMap.antilipschitz_of_boundproof · cited by 2
- ContinuousLinearMap.isUniformEmbedding_of_boundproof · cited by 1
- LinearMap.antilipschitz_of_comap_nhds_leproof · cited by 1
- antilipschitzWith_iff_exists_mul_le_normproof · cited by 1
- antilipschitz_of_bound_of_norm_oneproof · cited by 0