Theorems · Definition · functional analysis

ContinuousLinearEquiv.toHomeomorph

{R₁ : Type u_1} →
  {R₂ : Type u_2} →
    [inst : Semiring R₁] →
      [inst_1 : Semiring R₂] →
        {σ₁₂ : R₁ →+* R₂} →
          {σ₂₁ : R₂ →+* R₁} →
            [inst_2 : RingHomInvPair σ₁₂ σ₂₁] →
              [inst_3 : RingHomInvPair σ₂₁ σ₁₂] →
                {M₁ : Type u_4} →
                  [inst_4 : TopologicalSpace M₁] →
                    [inst_5 : AddCommMonoid M₁] →
                      {M₂ : Type u_5} →
                        [inst_6 : TopologicalSpace M₂] →
                          [inst_7 : AddCommMonoid M₂] →
                            [inst_8 : Module R₁ M₁] → [inst_9 : Module R₂ M₂] → (M₁ ≃SL[σ₁₂] M₂) → M₁ ≃ₜ M₂

A continuous linear equivalence induces a homeomorphism.

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

44 results in Mathlib

Foundations

Depth 17 from the axioms · uses no axioms

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModule