Theorems · Theorem · global analysis

contDiffWithinAt_localInvariantProp

∀ {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} {E' : Type u_5}
  [inst_4 : NormedAddCommGroup E'] [inst_5 : NormedSpace 𝕜 E'] {H' : Type u_6} [inst_6 : TopologicalSpace H']
  {I' : ModelWithCorners 𝕜 E' H'} (n : WithTop ℕ∞),
  (contDiffGroupoid n I).LocalInvariantProp (contDiffGroupoid n I') (ContDiffWithinAtProp I I' n)

Being Cⁿ in the model space is a local property, invariant under C^n maps. Therefore, it lifts nicely to manifolds.

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Defs

Cited by

29 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpace