Theorems · Definition · functional analysis

ContinuousAlternatingMap.toContinuousMultilinearMapLinear

{R : Type u_1} →
  {A : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        {ι : Type u_5} →
          [inst : Semiring R] →
            [inst_1 : Semiring A] →
              [inst_2 : AddCommMonoid M] →
                [inst_3 : AddCommMonoid N] →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : TopologicalSpace N] →
                      [inst_6 : ContinuousAdd N] →
                        [inst_7 : Module A M] →
                          [inst_8 : Module A N] →
                            [inst_9 : Module R N] →
                              [inst_10 : ContinuousConstSMul R N] →
                                [inst_11 : SMulCommClass A R N] →
                                  M [⋀^ι]→L[A] N →ₗ[R] ContinuousMultilinearMap A (fun x => M) N

Linear map version of the map toMultilinearMap associating to a continuous alternating map the corresponding multilinear map.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidTopologicalSpaceTopologicalSpaceContinuousAddModuleModuleModuleContinuousConstSMulSMulCommClass