Theorems · Theorem · global analysis

OpenPartialHomeomorph.extend_image_nhds_mem_nhds_of_boundaryless

∀ {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} [I.Boundaryless] {x : M},
  x ∈ f.source → ∀ {s : Set M}, s ∈ nhds x → ↑(f.extend I) '' s ∈ nhds (↑(f.extend I) x)

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

1 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceModelWithCorners.Boundaryless