Theorems · Theorem · general topology
hasBasis_nhdsSet_Iic_Iic
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α] (a : α)
[(nhdsWithin a (Set.Ioi a)).NeBot], (nhdsSet (Set.Iic a)).HasBasis (fun x => a < x) Set.Iic- Defined in
- Mathlib.Topology.Order.NhdsSet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Set.Elemproof · cited by 7,166
- nhdsWithinstatement and proof · cited by 1,912
- Set.Ioistatement and proof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Set.Iicstatement · cited by 1,111
- Filter.NeBotstatement and proof · cited by 853
- Filter.HasBasisstatement · cited by 604
- nhdsSetstatement · cited by 267
- self_mem_nhdsWithinproof · cited by 215
- Set.Nonempty.to_subtypeproof · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- Iic_mem_nhdsSet_Iic_iffproof · cited by 1
- hasBasis_nhdsSet_Ici_Iciproof · cited by 0