Theorems · Theorem · global analysis

mfderiv_extChartAt_self

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] [IsManifold I 1 M] {x : M},
  mfderiv% ↑(extChartAt I x) x = ContinuousLinearMap.id 𝕜 (TangentSpace I x)

The manifold derivative of extChartAt at the basepoint is the identity.

Defined in

Mathlib.Geometry.Manifold.MFDeriv.Atlas

Cited by

1 results in Mathlib

Foundations

Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold