Theorems · Definition · geometry

ContinuousAffineEquiv.toHomeomorph

{k : Type u_1} →
  {P₁ : Type u_2} →
    {P₂ : Type u_3} →
      {V₁ : Type u_6} →
        {V₂ : Type u_7} →
          [inst : Ring k] →
            [inst_1 : AddCommGroup V₁] →
              [inst_2 : Module k V₁] →
                [inst_3 : AddTorsor V₁ P₁] →
                  [inst_4 : TopologicalSpace P₁] →
                    [inst_5 : AddCommGroup V₂] →
                      [inst_6 : Module k V₂] →
                        [inst_7 : AddTorsor V₂ P₂] → [inst_8 : TopologicalSpace P₂] → (P₁ ≃ᴬ[k] P₂) → P₁ ≃ₜ P₂

A continuous affine equivalence is a homeomorphism.

Defined in

Mathlib.Topology.Algebra.ContinuousAffineEquiv

Cited by

8 results in Mathlib

Foundations

Depth 10 from the axioms · uses no axioms

Assumes

RingAddCommGroupModuleAddTorsorTopologicalSpaceAddCommGroupModuleAddTorsorTopologicalSpace