Theorems · Definition · global analysis

NormedSpace.fromTangentSpace

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] → (v : E) → TangentSpace (modelWithCornersSelf 𝕜 E) v ≃L[𝕜] E

Identifying the tangent space at a normed space with the normed space itself. This canonical identification (which, in mathlib, is implemented using an abuse of definitional equality) is very prevalent in a number of places: this device allows making it explicit.

Defined in

Mathlib.Geometry.Manifold.IsManifold.Basic

Cited by

17 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace