Theorems · Theorem · general topology
frontier_eq_inter_compl_interior
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, frontier s = (interior s)ᶜ ∩ (interior sᶜ)ᶜ- Defined in
- Mathlib.Topology.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 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.
Cites10
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.complstatement and proof · cited by 2,925
- closureproof · cited by 1,254
- interiorstatement and proof · cited by 714
- frontierstatement and proof · cited by 214
- Set.sdiff_eqproof · cited by 59
- closure_complproof · cited by 19
- frontier_complproof · cited by 10
- closure_sdiff_interiorproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- compl_frontier_eq_union_interiorproof · cited by 2