Theorems · Theorem · general topology
lipschitzOnWith_iff_norm_div_le
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedCommGroup E] [inst_1 : SeminormedCommGroup F] {f : E → F} {C : NNReal}
{s : Set E}, LipschitzOnWith C f s ↔ ∀ ⦃x : E⦄, x ∈ s → ∀ ⦃y : E⦄, y ∈ s → ‖f x / f y‖ ≤ ↑C * ‖x / y‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- SeminormedCommGroupstatement and proof · cited by 191
- LipschitzOnWithstatement and proof · cited by 164
- lipschitzOnWith_iff_norm_inv_mul_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LipschitzOnWith.norm_div_leproof · cited by 1