Theorems · Theorem · global analysis

OpenPartialHomeomorph.extend_coord_change_source_mem_nhdsWithin

Deprecated since 2026-02-16Use ModelWithCorners.extendCoordChange_source_mem_nhdsWithin instead.

∀ {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} {e e' : OpenPartialHomeomorph M H} {x : E},
  x ∈ (ModelWithCorners.extendCoordChange e e').source →
    (ModelWithCorners.extendCoordChange e e').source ∈ nhdsWithin x (Set.range ↑I)

Alias of ModelWithCorners.extendCoordChange_source_mem_nhdsWithin.

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpace