Theorems · Definition · functional analysis

ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv

{R : Type u_1} →
  {M : Type u_2} →
    {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 N] →
                    [inst_5 : Module R N] →
                      [inst_6 : TopologicalSpace N] →
                        [inst_7 : AddCommMonoid N'] →
                          [inst_8 : Module R N'] →
                            [inst_9 : TopologicalSpace N'] → (N ≃L[R] N') → M [⋀^ι]→L[R] N ≃ M [⋀^ι]→L[R] N'

A continuous linear equivalence of codomains defines an equivalence between continuous alternating maps.

Defined in

Mathlib.Topology.Algebra.Module.Alternating.Basic

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpaceAddCommMonoidModuleTopologicalSpace