Theorems · Theorem · global analysis

ModelWithCorners.isClosed_boundary

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {n : WithTop ℕ∞} [IsManifold I n M],
  n ≠ 0 → IsClosed (ModelWithCorners.boundary M)

The boundary of any C¹ manifold is closed. This is currently only proven for C¹ manifolds, but holds at least for finite-dimensional topological manifolds too; see ModelWithCorners.isInteriorPoint_iff_of_mem_atlas.

Defined in

Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary

Cited by

0 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold