Theorems · Definition · functional analysis

ContinuousLinearEquiv.continuousAlternatingMapCongr

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {E' : Type u_3} →
      {F : Type u_4} →
        {G : Type u_5} →
          {ι : Type u_6} →
            [inst : NormedField 𝕜] →
              [inst_1 : AddCommGroup E] →
                [inst_2 : Module 𝕜 E] →
                  [inst_3 : TopologicalSpace E] →
                    [inst_4 : AddCommGroup E'] →
                      [inst_5 : Module 𝕜 E'] →
                        [inst_6 : TopologicalSpace E'] →
                          [inst_7 : AddCommGroup F] →
                            [inst_8 : Module 𝕜 F] →
                              [inst_9 : TopologicalSpace F] →
                                [inst_10 : IsTopologicalAddGroup F] →
                                  [inst_11 : ContinuousConstSMul 𝕜 F] →
                                    [inst_12 : AddCommGroup G] →
                                      [inst_13 : Module 𝕜 G] →
                                        [inst_14 : TopologicalSpace G] →
                                          [inst_15 : IsTopologicalAddGroup G] →
                                            [inst_16 : ContinuousConstSMul 𝕜 G] →
                                              (E ≃L[𝕜] E') → (F ≃L[𝕜] G) → E [⋀^ι]→L[𝕜] F ≃L[𝕜] E' [⋀^ι]→L[𝕜] G

Continuous linear equivalences between the domains and the codomains generate a continuous linear equivalence between the spaces of continuous alternating maps.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Topology

Cited by

2 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul