Theorems · Theorem · functional analysis

ContinuousLinearMap.continuousOn_uncurry_of_multilinear

∀ {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} {F : Type u_4} [inst : NormedField 𝕜] [Finite ι]
  [inst_2 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)]
  [inst_4 : TopologicalSpace F] [inst_5 : AddCommGroup F] [inst_6 : IsTopologicalAddGroup F] [inst_7 : Module 𝕜 F]
  {G : Type u_5} [inst_8 : AddCommGroup G] [inst_9 : TopologicalSpace G] [inst_10 : Module 𝕜 G]
  [inst_11 : ContinuousConstSMul 𝕜 F] (f : G →L[𝕜] ContinuousMultilinearMap 𝕜 E F) {s : Set (G × ((i : ι) → E i))},
  ContinuousOn (fun p => (f p.1) p.2) s

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

0 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldFiniteSeminormedAddCommGroupNormedSpaceTopologicalSpaceAddCommGroupIsTopologicalAddGroupModuleAddCommGroupTopologicalSpaceModuleContinuousConstSMul