Theorems · Theorem · general topology
HolderWith.uniformContinuous
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {C r : NNReal}
{f : X → Y}, HolderWith C r f → 0 < r → UniformContinuous fA Hölder continuous function is uniformly continuous
- Defined in
- Mathlib.Topology.MetricSpace.Holder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 211 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.
- NNRealstatement and proof · cited by 4,310
- Set.univproof · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- UniformContinuousstatement · cited by 410
- HolderWithstatement and proof · cited by 47
- HolderWith.holderOnWithproof · cited by 8
- uniformContinuousOn_univproof · cited by 4
- HolderOnWith.uniformContinuousOnproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- HolderWith.continuousproof · cited by 0