Theorems · Theorem · global analysis

ModelWithCorners.isBoundaryPoint_iff

∀ {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] {x : M},
  I.IsBoundaryPoint x ↔ ↑(extChartAt I x) x ∈ frontier (Set.range ↑I)

Defined in

Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace