Theorems · Theorem · general topology

AddMonoidHom.compLeftContinuousBounded_apply

∀ {β : Type v} {γ : Type w} (α : Type u_3) [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
  [inst_2 : AddMonoid β] [inst_3 : BoundedAdd β] [inst_4 : ContinuousAdd β] [inst_5 : PseudoMetricSpace γ]
  [inst_6 : AddMonoid γ] [inst_7 : BoundedAdd γ] [inst_8 : ContinuousAdd γ] (g : β →+ γ) {C : NNReal}
  (hg : LipschitzWith C ⇑g) (f : BoundedContinuousFunction α β),
  (AddMonoidHom.compLeftContinuousBounded α g hg) f = BoundedContinuousFunction.comp (⇑g) hg f

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

0 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpaceAddMonoidBoundedAddContinuousAddPseudoMetricSpaceAddMonoidBoundedAddContinuousAdd