Theorems · Theorem · general topology

LipschitzWith.comp

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β]
  [inst_2 : PseudoEMetricSpace γ] {Kf Kg : NNReal} {f : β → γ} {g : α → β},
  LipschitzWith Kf f → LipschitzWith Kg g → LipschitzWith (Kf * Kg) (f ∘ g)

The composition of Lipschitz functions is Lipschitz.

Defined in

Mathlib.Topology.EMetricSpace.Lipschitz

Cited by

11 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpacePseudoEMetricSpacePseudoEMetricSpace