Mathlib Map

Theorems · Inductive type · general topology

Dilation

(α : Type u_1) → (β : Type u_2) → [PseudoEMetricSpace α] → [PseudoEMetricSpace β] → Type (max u_1 u_2)

A dilation is a map that uniformly scales the edistance between any two points.

Defined in
Mathlib.Topology.MetricSpace.Dilation
Cited by
44 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
PseudoEMetricSpacePseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Dilation.comp · cited by 10Dilation.compIsometry.toDilation · cited by 8Isometry.toDilationDilation.ext · cited by 8Dilation.extDilationEquiv.trans · cited by 7DilationEquiv.transDilation.id · cited by 5Dilation.idDilation.ratio_comp' · cited by 3Dilation.ratio_comp'DilationEquiv.mulLeft · cited by 3DilationEquiv.mulLeftDilationEquiv.mulRight · cited by 3DilationEquiv.mulRightDilationEquiv.toDilation · cited by 3DilationEquiv.toDilationDilation.copy · cited by 2Dilation.copyDilation.mkOfDistEq · cited by 2Dilation.mkOfDistEqDilation.mkOfNNDistEq · cited by 2Dilation.mkOfNNDistEqDilation.mulLeft · cited by 2Dilation.mulLeftDilation.mulRight · cited by 2Dilation.mulRightDilation.ratioHom · cited by 2Dilation.ratioHomPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceDilationCITED BYCITES

Cites1

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by64

Results whose statement or proof uses this declaration.