Theorems · Theorem · general topology

AntilipschitzWith.isBounded_of_image2_left

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β]
  [inst_2 : PseudoMetricSpace γ] (f : α → β → γ) {K₁ : NNReal},
  (∀ (b : β), AntilipschitzWith K₁ fun a => f a b) →
    ∀ {s : Set α} {t : Set β}, Bornology.IsBounded (Set.image2 f s t) → Bornology.IsBounded s ∨ Bornology.IsBounded t

Defined in

Mathlib.Topology.MetricSpace.Antilipschitz

Cited by

3 results in Mathlib

Foundations

Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpacePseudoMetricSpacePseudoMetricSpace