Theorems · Definition · general topology

BoundedContinuousFunction.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} → LipschitzWith C G → BoundedContinuousFunction α β → BoundedContinuousFunction α γ

Composition (in the target) of a bounded continuous function with a Lipschitz map again gives a bounded continuous function.

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

12 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpacePseudoMetricSpace