Theorems · Theorem · general topology
frontier_Ici
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
[NoMinOrder α] {a : α}, frontier (Set.Ici a) = {a}- Defined in
- Mathlib.Topology.Order.DenselyOrdered
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- OrderTopologystatement and proof · cited by 1,355
- Set.Icistatement · cited by 1,070
- DenselyOrderedstatement and proof · cited by 471
- NoMinOrderstatement and proof · cited by 247
- frontierstatement · cited by 214
- Set.nonempty_Iioproof · cited by 10
- frontier_Ici'proof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Complex.frontier_setOfPred_le_improof · cited by 1
- Complex.frontier_setOfPred_le_reproof · cited by 1
- Complex.frontier_setOfPred_le_re_and_im_leproof · cited by 1
- Complex.frontier_setOfPred_le_re_and_le_improof · cited by 1