Theorems · Definition · geometry

ContinuousAffineEquiv.vaddConst

(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] →
                [inst_5 : TopologicalSpace V₁] → [IsTopologicalAddTorsor P₁] → P₁ → V₁ ≃ᴬ[k] P₁

The affine homeomorphism V ≃ᴬ[k] P given by v ↦ v +ᵥ p. This is Equiv.vaddConst as a ContinuousAffineEquiv.

Defined in

Mathlib.Topology.Algebra.ContinuousAffineEquiv

Cited by

3 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModuleAddTorsorTopologicalSpaceTopologicalSpaceIsTopologicalAddTorsor