Theorems · Definition · functional analysis

ContinuousLinearEquiv.arrowCongr

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

A pair of continuous linear equivalences generates a continuous linear equivalence between the spaces of continuous linear maps.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

16 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupAddCommGroupAddCommGroupNormedFieldModuleModuleModuleModuleTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupContinuousConstSMulContinuousConstSMul