Theorems · Definition · functional analysis

ContinuousLinearEquiv.continuousAlternatingMapCongrEquiv

{R : Type u_1} →
  {M : Type u_2} →
    {M' : Type u_3} →
      {N : Type u_4} →
        {N' : Type u_5} →
          {ι : Type u_6} →
            [inst : Semiring R] →
              [inst_1 : AddCommMonoid M] →
                [inst_2 : Module R M] →
                  [inst_3 : TopologicalSpace M] →
                    [inst_4 : AddCommMonoid M'] →
                      [inst_5 : Module R M'] →
                        [inst_6 : TopologicalSpace M'] →
                          [inst_7 : AddCommMonoid N] →
                            [inst_8 : Module R N] →
                              [inst_9 : TopologicalSpace N] →
                                [inst_10 : AddCommMonoid N'] →
                                  [inst_11 : Module R N'] →
                                    [inst_12 : TopologicalSpace N'] →
                                      (M ≃L[R] M') → (N ≃L[R] N') → M [⋀^ι]→L[R] N ≃ M' [⋀^ι]→L[R] N'

Continuous linear equivalences between domains and codomains define an equivalence between the spaces of continuous alternating maps.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpace