Theorems · Theorem · functional analysis

ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply

∀ {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂] {σ : 𝕜₁ →+* 𝕜₂} {E : Type u_3}
  {F : Type u_4} [inst_2 : AddCommGroup E] [inst_3 : Module 𝕜₁ E] [inst_4 : TopologicalSpace E]
  [inst_5 : IsTopologicalAddGroup E] [inst_6 : ContinuousSMul 𝕜₁ E] [inst_7 : AddCommGroup F] [inst_8 : Module 𝕜₂ F]
  [inst_9 : TopologicalSpace F] [inst_10 : IsTopologicalAddGroup F] [inst_11 : ContinuousSMul 𝕜₂ F]
  [inst_12 : T1Space E] [inst_13 : MontelSpace 𝕜₁ E] (f : CompactConvergenceCLM σ E F) (x : E),
  ((ContinuousLinearEquiv.toCompactConvergenceCLM σ E F).symm f) x = f x

Defined in

Mathlib.Analysis.LocallyConvex.Montel

Cited by

0 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousSMulAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousSMulT1SpaceMontelSpace