Theorems · Theorem · general topology
nhdsSet_Ici
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderClosedTopology α] {a : α},
nhdsSet (Set.Ici a) = nhds a ⊔ Filter.principal (Set.Ioi a)- Defined in
- Mathlib.Topology.Order.NhdsSet
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.Ioistatement and proof · cited by 1,463
- Set.Icistatement · cited by 1,070
- Filter.principalstatement and proof · cited by 740
- OrderClosedTopologystatement and proof · cited by 445
- nhdsSetstatement and proof · cited by 267
- Set.Ioi_insertproof · cited by 5
- nhdsSet_insertproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- nhdsSet_Iicproof · cited by 1