Theorems · Theorem · functional analysis

ContinuousMultilinearMap.prod_apply

∀ {R : Type u} {ι : Type v} {M₁ : ι → Type w₁} {M₂ : Type w₂} {M₃ : Type w₃} [inst : Semiring R]
  [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : AddCommMonoid M₂] [inst_3 : AddCommMonoid M₃]
  [inst_4 : (i : ι) → Module R (M₁ i)] [inst_5 : Module R M₂] [inst_6 : Module R M₃]
  [inst_7 : (i : ι) → TopologicalSpace (M₁ i)] [inst_8 : TopologicalSpace M₂] [inst_9 : TopologicalSpace M₃]
  (f : ContinuousMultilinearMap R M₁ M₂) (g : ContinuousMultilinearMap R M₁ M₃) (m : (i : ι) → M₁ i),
  (f.prod g) m = (f m, g m)

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleTopologicalSpaceTopologicalSpaceTopologicalSpace