Theorems · Theorem · functional analysis

ContinuousMultilinearMap.completeSpace

∀ {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} {F : Type u_4} [inst : NormedField 𝕜]
  [inst_1 : (i : ι) → TopologicalSpace (E i)] [inst_2 : (i : ι) → AddCommGroup (E i)]
  [inst_3 : (i : ι) → Module 𝕜 (E i)] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F] [inst_6 : UniformSpace F]
  [inst_7 : IsUniformAddGroup F] [∀ (i : ι), ContinuousSMul 𝕜 (E i)] [ContinuousConstSMul 𝕜 F] [CompleteSpace F],
  Topology.IsCoherentWith {s | Bornology.IsVonNBounded 𝕜 s} → CompleteSpace (ContinuousMultilinearMap 𝕜 E F)

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Topology

Cited by

1 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldTopologicalSpaceAddCommGroupModuleAddCommGroupModuleUniformSpaceIsUniformAddGroupContinuousSMulContinuousConstSMulCompleteSpace