Theorems · Theorem · general topology

Dilation.ratio_unique

∀ {α : Type u_1} {β : Type u_2} {F : Type u_4} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β]
  [inst_2 : FunLike F α β] [inst_3 : DilationClass F α β] {f : F} {x y : α} {r : NNReal},
  edist x y ≠ 0 → edist x y ≠ ⊤ → edist (f x) (f y) = ↑r * edist x y → r = Dilation.ratio f

The ratio is equal to the distance ratio for any two points with nonzero finite distance. dist and nndist versions below

Defined in

Mathlib.Topology.MetricSpace.Dilation

Cited by

3 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpaceFunLikeDilationClass