Theorems · Theorem · general topology
antilipschitzWith_iff_exists_mul_le_norm
∀ {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, AntilipschitzWith K ⇑f) ↔ ∃ c > 0, ∀ (x : E), c * ‖x‖ ≤ ‖f x‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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 and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- one_mulproof · cited by 2,841
- FunLikestatement and proof · cited by 2,560
- Nat.cast_oneproof · cited by 2,501
- le_reflproof · cited by 2,061
- mul_assocproof · cited by 1,667
- map_zeroproof · cited by 1,614
- LT.lt.ne'proof · cited by 1,417
- NNReal.toRealproof · cited by 1,260
Cited by1
Results whose statement or proof uses this declaration.
- IsCompactOperator.antilipschitz_of_not_hasEigenvalueproof · cited by 1