Theorems · Theorem · functional analysis

ContinuousMultilinearMap.hasBasis_nhds_zero

∀ {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 : TopologicalSpace F]
  [inst_7 : IsTopologicalAddGroup F],
  (nhds 0).HasBasis (fun SV => Bornology.IsVonNBounded 𝕜 SV.1 ∧ SV.2 ∈ nhds 0) fun SV => {f | Set.MapsTo (⇑f) SV.1 SV.2}

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Topology

Cited by

2 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldTopologicalSpaceAddCommGroupModuleAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroup