Theorems · Theorem · global analysis

contDiffGroupoid_prod

∀ {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] {E' : Type u_5} {H' : Type u_6}
  [inst_4 : NormedAddCommGroup E'] [inst_5 : NormedSpace 𝕜 E'] [inst_6 : TopologicalSpace H']
  {I : ModelWithCorners 𝕜 E H} {I' : ModelWithCorners 𝕜 E' H'} {e : OpenPartialHomeomorph H H}
  {e' : OpenPartialHomeomorph H' H'},
  e ∈ contDiffGroupoid n I → e' ∈ contDiffGroupoid n I' → e.prod e' ∈ contDiffGroupoid n (I.prod I')

The product of two C^n open partial homeomorphisms is C^n.

Defined in

Mathlib.Geometry.Manifold.IsManifold.Basic

Cited by

1 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpace