Theorems · Definition · global analysis
ModelWithCorners.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 : TopologicalSpace M] → [ChartedSpace H M] → Set MThe boundary of a manifold M is the set of its boundary points.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredproof · cited by 6,101
- ModelWithCornersstatement and proof · cited by 2,462
- ChartedSpacestatement and proof · cited by 2,397
- ModelWithCorners.IsBoundaryPointproof · cited by 11
Cited by19
Results whose statement or proof uses this declaration.
- ModelWithCorners.compl_interiorstatement · cited by 6
- ModelWithCorners.Boundaryless.boundary_eq_emptystatement · cited by 4
- ModelWithCorners.boundary_prodstatement and proof · cited by 2
- IsLocalDiffeomorph.preimage_boundarystatement and proof · cited by 2
- ModelWithCorners.boundary_of_boundaryless_leftstatement and proof · cited by 1
- ModelWithCorners.compl_boundarystatement · cited by 1
- Diffeomorph.preimage_boundarystatement · cited by 1
- ModelWithCorners.disjoint_interior_boundarystatement and proof · cited by 1
- IsLocalDiffeomorphOn.preimage_boundary_interstatement and proof · cited by 1
- ModelWithCorners.interior_union_boundary_eq_univstatement and proof · cited by 1
- ModelWithCorners.Boundaryless.iff_boundary_eq_emptystatement and proof · cited by 1
- boundary_Iccstatement and proof · cited by 1