Theorems · Theorem · general topology
disjoint_interior_frontier
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, Disjoint (interior s) (frontier s)Interior and frontier are disjoint.
- Defined in
- Mathlib.Topology.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Compl.complproof · cited by 2,925
- Disjointstatement · cited by 2,201
- closureproof · cited by 1,254
- interiorstatement and proof · cited by 714
- Set.inter_commproof · cited by 291
- frontierstatement · cited by 214
- Set.inter_assocproof · cited by 67
- Set.sdiff_eqproof · cited by 59
- Set.disjoint_iff_inter_eq_emptyproof · cited by 49
- Set.empty_interproof · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- ModelWithCorners.isInteriorPoint_iff_not_isBoundaryPointproof · cited by 2
- ModelWithCorners.disjoint_interior_boundaryproof · cited by 1