Theorems · Theorem · global analysis

OpenPartialHomeomorph.map_extend_nhds

∀ {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} {x : M},
  x ∈ f.source → Filter.map (↑(f.extend I)) (nhds x) = nhdsWithin (↑(f.extend I) x) (Set.range ↑I)

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

6 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace