Theorems · Definition · geometry

AffineIsometryEquiv.vaddConst

(𝕜 : Type u_1) →
  {V : Type u_2} →
    {P : Type u_10} →
      [inst : NormedField 𝕜] →
        [inst_1 : SeminormedAddCommGroup V] →
          [inst_2 : NormedSpace 𝕜 V] → [inst_3 : PseudoMetricSpace P] → [inst_4 : NormedAddTorsor V P] → P → V ≃ᵃⁱ[𝕜] P

The map v ↦ v +ᵥ p as an affine isometric equivalence between V and P.

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

8 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor