Theorems · Definition · functional analysis

ContinuousAlternatingMap.toContinuousMultilinearMapCLM

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      {ι : Type u_4} →
        [inst : NormedField 𝕜] →
          [inst_1 : AddCommGroup E] →
            [inst_2 : Module 𝕜 E] →
              [inst_3 : TopologicalSpace E] →
                [inst_4 : AddCommGroup F] →
                  [inst_5 : Module 𝕜 F] →
                    [inst_6 : TopologicalSpace F] →
                      [inst_7 : IsTopologicalAddGroup F] →
                        (R : Type u_5) →
                          [inst_8 : Semiring R] →
                            [inst_9 : Module R F] →
                              [inst_10 : ContinuousConstSMul R F] →
                                [inst_11 : SMulCommClass 𝕜 R F] →
                                  E [⋀^ι]→L[𝕜] F →L[R] ContinuousMultilinearMap 𝕜 (fun x => E) F

The inclusion of alternating continuous multilinear maps into continuous multilinear maps as a continuous linear map.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Topology

Cited by

8 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupSemiringModuleContinuousConstSMulSMulCommClass