Theorems · Theorem · general topology

LipschitzWith.prodMk

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β]
  [inst_2 : PseudoEMetricSpace γ] {f : α → β} {Kf : NNReal},
  LipschitzWith Kf f → ∀ {g : α → γ} {Kg : NNReal}, LipschitzWith Kg g → LipschitzWith (max Kf Kg) fun x => (f x, g x)

If f and g are Lipschitz functions, so is the induced map f × g to the product type.

Defined in

Mathlib.Topology.EMetricSpace.Lipschitz

Cited by

4 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpacePseudoEMetricSpace