Theorems · Definition · functional analysis

FormalMultilinearSeries.pi

{𝕜 : Type u} →
  {E : Type v} →
    [inst : Semiring 𝕜] →
      [inst_1 : AddCommMonoid E] →
        [inst_2 : Module 𝕜 E] →
          [inst_3 : TopologicalSpace E] →
            [inst_4 : ContinuousAdd E] →
              [inst_5 : ContinuousConstSMul 𝕜 E] →
                {ι : Type u_1} →
                  {F : ι → Type u_2} →
                    [inst_6 : (i : ι) → AddCommGroup (F i)] →
                      [inst_7 : (i : ι) → Module 𝕜 (F i)] →
                        [inst_8 : (i : ι) → TopologicalSpace (F i)] →
                          [inst_9 : ∀ (i : ι), IsTopologicalAddGroup (F i)] →
                            [inst_10 : ∀ (i : ι), ContinuousConstSMul 𝕜 (F i)] →
                              ((i : ι) → FormalMultilinearSeries 𝕜 E (F i)) →
                                FormalMultilinearSeries 𝕜 E ((i : ι) → F i)

Product of formal multilinear series (with the same field 𝕜 and the same source space, but possibly different target spaces).

Defined in

Mathlib.Analysis.Calculus.FormalMultilinearSeries

Cited by

12 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMulAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul