Theorems · Definition · functional analysis

ContinuousMultilinearMap.pi

{R : Type u} →
  {ι : Type v} →
    {M₁ : ι → Type w₁} →
      [inst : Semiring R] →
        [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] →
          [inst_2 : (i : ι) → Module R (M₁ i)] →
            [inst_3 : (i : ι) → TopologicalSpace (M₁ i)] →
              {ι' : Type u_1} →
                {M' : ι' → Type u_2} →
                  [inst_4 : (i : ι') → AddCommMonoid (M' i)] →
                    [inst_5 : (i : ι') → TopologicalSpace (M' i)] →
                      [inst_6 : (i : ι') → Module R (M' i)] →
                        ((i : ι') → ContinuousMultilinearMap R M₁ (M' i)) →
                          ContinuousMultilinearMap R M₁ ((i : ι') → M' i)

Combine a family of continuous multilinear maps with the same domain and codomains M' i into a continuous multilinear map taking values in the space of functions ∀ i, M' i.

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

10 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidTopologicalSpaceModule