Theorems · Definition · functional analysis

ContinuousAlternatingMap.compContinuousLinearMapCLM

{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] →
                        [inst_8 : ContinuousConstSMul 𝕜 F] →
                          {E' : Type u_6} →
                            [inst_9 : AddCommGroup E'] →
                              [inst_10 : Module 𝕜 E'] →
                                [inst_11 : TopologicalSpace E'] → (E →L[𝕜] E') → E' [⋀^ι]→L[𝕜] F →L[𝕜] E [⋀^ι]→L[𝕜] F

Composition of a continuous alternating map and a continuous linear map as a bundled continuous linear map. Note that for general topological vector spaces, this function does not need to be continuous in f.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Topology

Cited by

12 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulAddCommGroupModuleTopologicalSpace