Theorems · Theorem · global analysis

contMDiffOn_isOpenEmbedding_symm

∀ {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] {e : M → H} (h : Topology.IsOpenEmbedding e) {n : WithTop ℕ∞} [inst_5 : Nonempty M],
  ContMDiffOn I I n (↑(Topology.IsOpenEmbedding.toOpenPartialHomeomorph e h).symm) (Set.range e)

If the ChartedSpace structure on a manifold M is given by an open embedding e : M → H, then the inverse of e is C^n.

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Basic

Cited by

1 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceNonempty