Theorems · Theorem · functional analysis

ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {ι : Type u_4} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
  [inst_6 : TopologicalSpace F] [inst_7 : IsTopologicalAddGroup F] {ι' : Type u_5} {p : ι' → Prop} {b : ι' → 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.Alternating.Topology

Cited by

1 results in Mathlib

Foundations

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

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroup