Theorems · Theorem · general topology

Dilation.diam_image

∀ {α : Type u_1} {β : Type u_2} {F : Type u_4} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β]
  [inst_2 : FunLike F α β] [inst_3 : DilationClass F α β] (f : F) (s : Set α),
  Metric.diam (⇑f '' s) = ↑(Dilation.ratio f) * Metric.diam s

A dilation scales the diameter by ratio f in pseudometric spaces.

Defined in

Mathlib.Topology.MetricSpace.Dilation

Cited by

1 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpacePseudoMetricSpaceFunLikeDilationClass