Theorems · Theorem · global analysis

contMDiffOn_symm_of_mem_maximalAtlas

∀ {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] {n : WithTop ℕ∞} {e : OpenPartialHomeomorph M H},
  e ∈ IsManifold.maximalAtlas I n M → ContMDiffOn I I n (↑e.symm) e.target

The inverse of an atlas member is C^n for any n.

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Atlas

Cited by

5 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace