Theorems · Theorem · general topology
Ioi_mem_nhdsSet_Ici_iff
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderClosedTopology α] {a b : α},
Set.Ioi a ∈ nhdsSet (Set.Ici b) ↔ a < b- Defined in
- Mathlib.Topology.Order.NhdsSet
- Cited by
- 2 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.
Cites11
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
- Filterstatement · cited by 8,121
- Set.Ioistatement · cited by 1,463
- Set.Icistatement · cited by 1,070
- OrderClosedTopologystatement and proof · cited by 445
- nhdsSetstatement · cited by 267
- isOpen_Ioiproof · cited by 43
- IsOpen.mem_nhdsSetproof · cited by 17
- Set.Ici_subset_Ioiproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Ioi_mem_nhdsSet_Iciproof · cited by 2
- Iio_mem_nhdsSet_Iic_iffproof · cited by 1