Theorems · Theorem · global analysis

nhdsWithin_extChartAt_target_eq

∀ {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]
  {I : ModelWithCorners 𝕜 E H} [inst_5 : ChartedSpace H M] (x : M),
  nhdsWithin (↑(extChartAt I x) x) (extChartAt I x).target = nhdsWithin (↑(extChartAt I x) x) (Set.range ↑I)

Around the image of the base point, the neighborhoods are the same within (extChartAt I x).target and within range I.

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

3 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace