Theorems · Theorem · functional analysis

CompactConvergenceCLM.piEquivL_symm_apply

∀ {𝕜₁ : Type u_1} [inst : NormedField 𝕜₁] {E : Type u_4} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜₁ E]
  [inst_3 : TopologicalSpace E] {ι : Type u_7} (F : ι → Type u_8) [inst_4 : (i : ι) → AddCommGroup (F i)]
  [inst_5 : (i : ι) → Module 𝕜₁ (F i)] [inst_6 : (i : ι) → TopologicalSpace (F i)]
  [inst_7 : ∀ (i : ι), IsTopologicalAddGroup (F i)] [inst_8 : ∀ (i : ι), ContinuousConstSMul 𝕜₁ (F i)]
  (T : CompactConvergenceCLM (RingHom.id 𝕜₁) E ((i : ι) → F i)) (e : E) (i : ι),
  ((CompactConvergenceCLM.piEquivL 𝕜₁ E F).symm T i) e = T e i

Defined in

Mathlib.Topology.Algebra.Module.Spaces.CompactConvergenceCLM

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul