Theorems · Theorem · global analysis

inCoordinates_tangent_bundle_core_model_space

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {H : Type u_4}
  [inst_5 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {H' : Type u_5} [inst_6 : TopologicalSpace H']
  {I' : ModelWithCorners 𝕜 E' H'} (x₀ x : H) (y₀ y : H') (ϕ : E →L[𝕜] E'),
  ContinuousLinearMap.inCoordinates E (TangentSpace I) E' (TangentSpace I') x₀ x y₀ y ϕ = ϕ

The map inCoordinates for the tangent bundle is trivial on the model spaces

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Tangent

Cited by

1 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace