Theorems · Definition · geometry

AffineIsometryEquiv.ofTop

{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] →
                (s₁ : AffineSubspace 𝕜 P) → [inst_5 : Nonempty ↥s₁] → s₁ = ⊤ → ↥s₁ ≃ᵃⁱ[𝕜] P

The identity equivalence of an affine subspace equal to ⊤ to the whole space.

Defined in

Mathlib.Analysis.Normed.Affine.Isometry

Cited by

2 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldSeminormedAddCommGroupNormedSpacePseudoMetricSpaceNormedAddTorsorNonempty