Theorems · Theorem · functional analysis

ContinuousMultilinearMap.cont

∀ {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]
  (self : ContinuousMultilinearMap R M₁ M₂), Continuous self.toFun

Continuous multilinear maps over the ring R, from ∀ i, M₁ i to M₂ where M₁ i and M₂ are modules over R with a topological structure. In applications, there will be compatibility conditions between the algebraic and the topological structures, but this is not needed for the definition.

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

6 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleTopologicalSpaceTopologicalSpace