Theorems · Theorem · functional analysis

ContinuousLinearMapWOT.continuous_of_dual_apply_continuous

∀ {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 : TopologicalSpace E] [inst_4 : Module 𝕜₁ E]
  [inst_5 : AddCommGroup F] [inst_6 : TopologicalSpace F] [inst_7 : Module 𝕜₂ F] [inst_8 : IsTopologicalAddGroup F]
  [inst_9 : ContinuousConstSMul 𝕜₂ F] {α : Type u_5} [inst_10 : TopologicalSpace α] {g : α → E →SWOT[σ] F},
  (∀ (x : E) (y : StrongDual 𝕜₂ F), Continuous fun a => y ((g a) x)) → Continuous g

Defined in

Mathlib.Analysis.LocallyConvex.WeakOperatorTopology

Cited by

3 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNormedFieldAddCommGroupTopologicalSpaceModuleAddCommGroupTopologicalSpaceModuleIsTopologicalAddGroupContinuousConstSMulTopologicalSpace