Theorems · Theorem · functional analysis

ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis

∀ {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] {ι_1 : Type u_5} {p : ι_1 → Prop} {b : ι_1 → Set F},
  (nhds 0).HasBasis p b →
    (nhds 0).HasBasis (fun Si => Bornology.IsVonNBounded 𝕜 Si.1 ∧ p Si.2) fun Si => {f | Set.MapsTo (⇑f) Si.1 (b Si.2)}

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Topology

Cited by

3 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldTopologicalSpaceAddCommGroupModuleAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroup