Theorems · Theorem · general topology
isClosed_frontier
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsClosed (frontier s)The frontier of a set is closed.
- Defined in
- Mathlib.Topology.Closure
- Cited by
- 2 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.
Cites7
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
- frontierstatement · cited by 214
- isClosed_closureproof · cited by 195
- IsClosed.interproof · cited by 61
- frontier_eq_closure_inter_closureproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_null_frontier_thickeningproof · cited by 3
- isClosed_intrinsicFrontierproof · cited by 0