Theorems · Theorem · general topology
PredOrder.hasBasis_nhds_Ico_of_exists_gt
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [PredOrder α] {a : α},
(∃ l, a < l) → (nhds a).HasBasis (fun x => a < x) fun x => Set.Ico a x- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- nhdsstatement · cited by 5,554
- OrderTopologystatement and proof · cited by 1,355
- Set.Icostatement · cited by 799
- Filter.HasBasisstatement · cited by 604
- PredOrderstatement and proof · cited by 334
- nhdsGE_basis_of_exists_gtproof · cited by 6
- PredOrder.nhdsGE_eq_nhdsproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- PredOrder.accPt_principalproof · cited by 2
- PredOrder.hasBasis_nhds_Icoproof · cited by 1
- PredOrder.hasBasis_nhds_Ioc_of_exists_gtproof · cited by 0
- PredOrder.isOpen_iffproof · cited by 0