Theorems · Theorem · global analysis

ModelWithCorners.Boundaryless.iff_boundary_eq_empty

∀ {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], ModelWithCorners.boundary M = ∅ ↔ BoundarylessManifold I M

M is boundaryless if and only if its boundary is empty.

Defined in

Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace