Theorems · Theorem · general topology
Isometry.lipschitz
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
Isometry f → LipschitzWith 1 f- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Eq.leproof · cited by 605
- LipschitzWithstatement · cited by 316
- Isometrystatement and proof · cited by 230
- LipschitzWith.of_edist_leproof · cited by 12
Cited by22
Results whose statement or proof uses this declaration.
- Isometry.continuousproof · cited by 23
- Isometry.isClosedEmbeddingproof · cited by 15
- Isometry.isUniformEmbeddingproof · cited by 4
- MeasureTheory.FiniteMeasure.tendsto_of_forall_integral_tendstoproof · cited by 3
- MeasureTheory.memLp_prod_iffproof · cited by 3
- Isometry.uniformContinuousproof · cited by 3
- MeasureTheory.memLp_pi_iffproof · cited by 2
- Isometry.dimH_imageproof · cited by 2
- Isometry.isCover_image_iffproof · cited by 1
- Bornology.IsBounded.smulproof · cited by 1
- LinearIsometry.lipschitzproof · cited by 1
- Bornology.IsBounded.vaddproof · cited by 1