Theorems · Definition · functional analysis

ContinuousMultilinearMap.constOfIsEmpty

(R : Type u) →
  {ι : Type v} →
    (M₁ : ι → Type w₁) →
      {M₂ : Type w₂} →
        [inst : Semiring R] →
          [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] →
            [inst_2 : AddCommMonoid M₂] →
              [inst_3 : (i : ι) → Module R (M₁ i)] →
                [inst_4 : Module R M₂] →
                  [inst_5 : (i : ι) → TopologicalSpace (M₁ i)] →
                    [inst_6 : TopologicalSpace M₂] → [IsEmpty ι] → M₂ → ContinuousMultilinearMap R M₁ M₂

The constant map is multilinear when ι is empty.

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

6 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleTopologicalSpaceTopologicalSpaceIsEmpty