Theorems · Definition · geometry

ContinuousAffineEquiv.constVAdd

(k : Type u_1) →
  (P₁ : Type u_2) →
    {V₁ : Type u_6} →
      [inst : Ring k] →
        [inst_1 : AddCommGroup V₁] →
          [inst_2 : Module k V₁] →
            [inst_3 : AddTorsor V₁ P₁] → [inst_4 : TopologicalSpace P₁] → [ContinuousConstVAdd V₁ P₁] → V₁ → P₁ ≃ᴬ[k] P₁

The map p ↦ v +ᵥ p as a continuous affine automorphism of an affine space on which addition is continuous.

Defined in

Mathlib.Topology.Algebra.ContinuousAffineEquiv

Cited by

3 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorTopologicalSpaceContinuousConstVAdd