Theorems · Theorem · general topology
Disjoint.frontier_left
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsOpen t → Disjoint s t → Disjoint (frontier s) t- Defined in
- Mathlib.Topology.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 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.
Cites11
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
- LE.le.transproof · cited by 3,151
- IsOpenstatement and proof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- frontierstatement · cited by 214
- Set.disjoint_leftproof · cited by 121
- closure_minimalproof · cited by 94
- isClosed_compl_iffproof · cited by 35
- Set.subset_compl_iff_disjoint_rightproof · cited by 17
- frontier_subset_closureproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Subalgebra.spectrum_sUnion_connectedComponentInproof · cited by 2
- Disjoint.frontier_rightproof · cited by 0