Theorems · Theorem · global analysis

symm_trans_mem_contDiffGroupoid

∀ {n : WithTop ℕ∞} {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 : OpenPartialHomeomorph M H), e.symm.trans e ∈ contDiffGroupoid n I

The composition of an open partial homeomorphism from H to M and its inverse belongs to the C^n groupoid.

Defined in

Mathlib.Geometry.Manifold.IsManifold.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace