Theorems · Inductive type · geometry

AffineIsometry

(𝕜 : Type u_1) →
  {V : Type u_2} →
    {V₂ : Type u_5} →
      (P : Type u_10) →
        (P₂ : Type u_11) →
          [inst : NormedField 𝕜] →
            [inst_1 : SeminormedAddCommGroup V] →
              [NormedSpace 𝕜 V] →
                [inst_3 : PseudoMetricSpace P] →
                  [NormedAddTorsor V P] →
                    [inst_5 : SeminormedAddCommGroup V₂] →
                      [NormedSpace 𝕜 V₂] →
                        [inst : PseudoMetricSpace P₂] →
                          [NormedAddTorsor V₂ P₂] → Type (max (max (max u_10 u_11) u_2) u_5)

A 𝕜-affine isometric embedding of one normed add-torsor over a normed 𝕜-space into another, denoted as f : P →ᵃⁱ[𝕜] P₂.

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

79 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsor