Theorems · Theorem · global analysis

ModelWithCorners.boundary_prod

∀ {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] {E' : Type u_5} [inst_6 : NormedAddCommGroup E']
  [inst_7 : NormedSpace 𝕜 E'] {H' : Type u_6} [inst_8 : TopologicalSpace H'] {N : Type u_7}
  [inst_9 : TopologicalSpace N] [inst_10 : ChartedSpace H' N] {J : ModelWithCorners 𝕜 E' H'},
  ModelWithCorners.boundary (M × N) =
    Set.univ.prod (ModelWithCorners.boundary N) ∪ (ModelWithCorners.boundary M).prod Set.univ

The boundary of M × N is ∂M × N ∪ (M × ∂N).

Defined in

Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary

Cited by

2 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace