Theorems · Definition · functional analysis

ContinuousLinearEquiv.toLinearEquiv

{R : Type u_1} →
  {S : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : Semiring S] →
        {σ : R →+* S} →
          {σ' : S →+* R} →
            [inst_2 : RingHomInvPair σ σ'] →
              [inst_3 : RingHomInvPair σ' σ] →
                {M : Type u_3} →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : AddCommMonoid M] →
                      {M₂ : Type u_4} →
                        [inst_6 : TopologicalSpace M₂] →
                          [inst_7 : AddCommMonoid M₂] →
                            [inst_8 : Module R M] → [inst_9 : Module S M₂] → (M ≃SL[σ] M₂) → M ≃ₛₗ[σ] M₂

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

118 results in Mathlib

Foundations

Depth 13 from the axioms, rests on 86 definitions · uses no axioms

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModule