Theorems · Theorem · global analysis

OpenPartialHomeomorph.map_extend_symm_nhdsWithin

∀ {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]
  (f : OpenPartialHomeomorph M H) {I : ModelWithCorners 𝕜 E H} {s : Set M} {y : M},
  y ∈ f.source →
    Filter.map (↑(f.extend I).symm) (nhdsWithin (↑(f.extend I) y) (↑(f.extend I).symm ⁻¹' s ∩ Set.range ↑I)) =
      nhdsWithin y s

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace