Theorems · Theorem · global analysis

VectorField.eventuallyEq_mpullback_mpullbackWithin_extChartAt

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {x : M} [IsManifold I 1 M]
  (V : (x : M) → TangentSpace I x),
  V =ᶠ[nhdsWithin x s]
    VectorField.mpullback I (modelWithCornersSelf 𝕜 E) (↑(extChartAt I x))
      (VectorField.mpullbackWithin (modelWithCornersSelf 𝕜 E) I (↑(extChartAt I x).symm) V (Set.range ↑I))

Defined in

Mathlib.Geometry.Manifold.VectorField.Pullback

Cited by

2 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceIsManifold