Theorems · Theorem · global analysis

ContDiffGroupoid.mem_of_source_eq_empty

∀ {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}
  (f : OpenPartialHomeomorph H H), f.source = ∅ → f ∈ contDiffGroupoid n I

Any change of coordinates with empty source belongs to contDiffGroupoid.

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

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpace