Theorems · Theorem · general topology
Iio_mem_nhdsSet_Ico
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderClosedTopology α] {a b c : α},
b ≤ c → Set.Iio c ∈ nhdsSet (Set.Ico a b)- Defined in
- Mathlib.Topology.Order.NhdsSet
- Cited by
- 3 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.
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.Iiostatement and proof · cited by 1,166
- Set.Icostatement · cited by 799
- OrderClosedTopologystatement and proof · cited by 445
- nhdsSetstatement · cited by 267
- nhdsSet_monoproof · cited by 18
- Set.Ico_subset_Iio_selfproof · cited by 8
- nhdsSet_Iioproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Iic_mem_nhdsSet_Icoproof · cited by 2
- Ioo_mem_nhdsSet_Icoproof · cited by 0
- Ico_mem_nhdsSet_Icoproof · cited by 0