Theorems · Theorem · general topology

LocallyLipschitz.prodMk

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

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

Defined in

Mathlib.Topology.EMetricSpace.Lipschitz

Cited by

2 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpacePseudoEMetricSpace