Theorems · Theorem · functional analysis

ContinuousLinearMap.piEquivL_symm_apply

∀ (𝕜 : Type u_1) [inst : NormedField 𝕜] (E : Type u_2) {ι : Type u_3} (F : ι → Type u_4) [inst_1 : AddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [inst_4 : (i : ι) → AddCommGroup (F i)]
  [inst_5 : (i : ι) → Module 𝕜 (F i)] [inst_6 : (i : ι) → TopologicalSpace (F i)]
  [inst_7 : ∀ (i : ι), IsTopologicalAddGroup (F i)] [inst_8 : ∀ (i : ι), ContinuousConstSMul 𝕜 (F i)]
  (f : E →L[𝕜] (i : ι) → F i) (i : ι), (ContinuousLinearMap.piEquivL 𝕜 E F).symm f i = ContinuousLinearMap.proj i ∘SL f

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

0 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul