Theorems · Theorem · general topology

bornology_eq_of_bilipschitz

∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K₁ K₂ : NNReal}
  {f : α → β}, AntilipschitzWith K₁ f → LipschitzWith K₂ f → Bornology.cobounded α = Bornology.cobounded α

If f : α → β is bilipschitz, then the pullback of the bornology on β through f agrees with the bornology on α.

Defined in

Mathlib.Topology.MetricSpace.Bilipschitz

Cited by

1 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpacePseudoMetricSpace