Theorems · Theorem · functional analysis

PointwiseConvergenceCLM.postcomp_apply

∀ {𝕜₁ : Type u_4} {𝕜₂ : Type u_5} {𝕜₃ : Type u_6} [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_7) {F : Type u_8} {G : Type u_10} [inst_4 : AddCommGroup E] [inst_5 : TopologicalSpace E]
  [inst_6 : AddCommGroup F] [inst_7 : TopologicalSpace F] [inst_8 : IsTopologicalAddGroup F] [inst_9 : AddCommGroup G]
  [inst_10 : TopologicalSpace G] [inst_11 : IsTopologicalAddGroup G] [inst_12 : Module 𝕜₁ E] [inst_13 : Module 𝕜₂ F]
  [inst_14 : Module 𝕜₃ G] [inst_15 : ContinuousConstSMul 𝕜₂ F] [inst_16 : ContinuousConstSMul 𝕜₃ G] (L : F →SL[τ] G)
  (f : E →SLₚₜ[σ] F), (PointwiseConvergenceCLM.postcomp E L) f = L ∘SL f

Defined in

Mathlib.Topology.Algebra.Module.Spaces.PointwiseConvergenceCLM

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldNormedFieldRingHomCompTripleAddCommGroupTopologicalSpaceAddCommGroupTopologicalSpaceIsTopologicalAddGroupAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleModuleModuleContinuousConstSMulContinuousConstSMul