Theorems · Definition · functional analysis

ContinuousLinearMap.coprodEquivL

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      {G : Type u_4} →
        (S : Type u_5) →
          [inst : NormedField 𝕜] →
            [inst_1 : Semiring S] →
              [inst_2 : AddCommGroup E] →
                [inst_3 : Module 𝕜 E] →
                  [inst_4 : TopologicalSpace E] →
                    [IsTopologicalAddGroup E] →
                      [inst_6 : AddCommGroup F] →
                        [inst_7 : Module 𝕜 F] →
                          [inst_8 : TopologicalSpace F] →
                            [IsTopologicalAddGroup F] →
                              [inst_10 : AddCommGroup G] →
                                [inst_11 : Module 𝕜 G] →
                                  [inst_12 : TopologicalSpace G] →
                                    [inst_13 : IsTopologicalAddGroup G] →
                                      [ContinuousConstSMul 𝕜 G] →
                                        [inst_15 : Module S G] →
                                          [inst_16 : SMulCommClass 𝕜 S G] →
                                            [inst_17 : ContinuousConstSMul S G] →
                                              ((E →L[𝕜] G) × (F →L[𝕜] G)) ≃L[S] E × F →L[𝕜] G

ContinuousLinearMap.coprod as a ContinuousLinearEquiv.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

2 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldSemiringAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulModuleSMulCommClassContinuousConstSMul