Theorems · Theorem · general topology
IsClosed.frontier_eq
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsClosed s → frontier s = s \ interior s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
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
- IsClosedstatement and proof · cited by 1,639
- interiorstatement and proof · cited by 714
- frontierstatement · cited by 214
- IsClosed.closure_eqproof · cited by 139
Cited by4
Results whose statement or proof uses this declaration.
- interior_frontierproof · cited by 3
- SeparatedNhds.of_isClosed_isCompact_closure_compl_isClosedproof · cited by 1
- frontier_sphereproof · cited by 0
- frontier_sphere'proof · cited by 0