Theorems · Theorem · functional analysis

ContinuousLinearMap.precompUniformConvergenceCLM_apply

∀ {𝕜₁ : Type u_6} {𝕜₂ : Type u_7} {𝕜₃ : Type u_8} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂]
  [inst_2 : NormedField 𝕜₃] {σ : 𝕜₁ →+* 𝕜₂} {τ : 𝕜₂ →+* 𝕜₃} {ρ : 𝕜₁ →+* 𝕜₃} [inst_3 : RingHomCompTriple σ τ ρ]
  {E : Type u_9} {F : Type u_10} (G : Type u_11) [inst_4 : AddCommGroup E] [inst_5 : Module 𝕜₁ E]
  [inst_6 : AddCommGroup F] [inst_7 : Module 𝕜₂ F] [inst_8 : AddCommGroup G] [inst_9 : Module 𝕜₃ G]
  [inst_10 : TopologicalSpace E] [inst_11 : TopologicalSpace F] [inst_12 : TopologicalSpace G] (𝔖 : Set (Set E))
  (𝔗 : Set (Set F)) [inst_13 : IsTopologicalAddGroup G] [inst_14 : ContinuousConstSMul 𝕜₃ G] (L : E →SL[σ] F)
  (hL : Set.MapsTo (fun x => ⇑L '' x) 𝔖 𝔗) (f : UniformConvergenceCLM τ G 𝔗),
  (ContinuousLinearMap.precompUniformConvergenceCLM G 𝔖 𝔗 L hL) f = f ∘SL L

Defined in

Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldNormedFieldRingHomCompTripleAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul