Theorems · Theorem · functional analysis

ContinuousLinearMapWOT.continuousAt_iff

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup E] [inst_2 : TopologicalSpace E]
  [inst_3 : Module 𝕜 E] [inst_4 : NormedAddCommGroup F] [inst_5 : InnerProductSpace 𝕜 F] [CompleteSpace F]
  {α : Type u_4} [inst_7 : TopologicalSpace α] {f : α → E →WOT[𝕜] F} {a : α},
  ContinuousAt f a ↔ ∀ (x : E) (y : F), ContinuousAt (fun x_1 => inner 𝕜 y ((f x_1) x)) a

Defined in

Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology

Cited by

2 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeAddCommGroupTopologicalSpaceModuleNormedAddCommGroupInnerProductSpaceCompleteSpaceTopologicalSpace