Theorems · Theorem · general topology
Isometry.antilipschitz
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β},
Isometry f → AntilipschitzWith 1 f- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 148 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
- one_mulproof · cited by 2,841
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.edistproof · cited by 735
- Isometrystatement and proof · cited by 230
- AntilipschitzWithstatement · cited by 132
Cited by14
Results whose statement or proof uses this declaration.
- Isometry.isClosedEmbeddingproof · cited by 15
- Isometry.injectiveproof · cited by 11
- Isometry.isUniformInducingproof · cited by 10
- Isometry.isUniformEmbeddingproof · cited by 4
- Isometry.dimH_imageproof · cited by 2
- LinearIsometry.antilipschitzproof · cited by 1
- IsSelfAdjoint.isConnected_spectrum_complproof · cited by 1
- AffineIsometryEquiv.antilipschitzproof · cited by 0
- AffineIsometry.antilipschitzproof · cited by 0
- IsometryClass.antilipschitzproof · cited by 0
- LinearIsometryEquiv.antilipschitzproof · cited by 0
- Bornology.IsBounded.of_addproof · cited by 0