Theorems · Theorem · global analysis

ModelWithCorners.contDiffOn_extendCoordChange

∀ {𝕜 : Type u_1} {E : Type u_2} {M : Type u_3} {H : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : TopologicalSpace H] [inst_4 : TopologicalSpace M]
  {n : WithTop ℕ∞} {I : ModelWithCorners 𝕜 E H} {e e' : OpenPartialHomeomorph M H} [inst_5 : ChartedSpace H M],
  e ∈ IsManifold.maximalAtlas I n M →
    e' ∈ IsManifold.maximalAtlas I n M →
      ContDiffOn 𝕜 n (↑(ModelWithCorners.extendCoordChange e e')) (ModelWithCorners.extendCoordChange e e').source

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

7 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace