Theorems · Theorem · general topology

BoundedContinuousFunction.uniformContinuous_comp

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
  [inst_2 : PseudoMetricSpace γ] {G : β → γ} {C : NNReal} (H : LipschitzWith C G),
  UniformContinuous (BoundedContinuousFunction.comp G H)

The composition operator (in the target) with a Lipschitz map is uniformly continuous.

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpacePseudoMetricSpacePseudoMetricSpace