Theorems · Theorem · general topology
Ici_mem_nhds
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIicTopology α] {a b : α},
a < b → Set.Ici a ∈ nhds b- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- nhdsstatement · cited by 5,554
- Set.Icistatement · cited by 1,070
- Filter.mem_of_supersetproof · cited by 308
- ClosedIicTopologystatement and proof · cited by 115
- Set.Ioi_subset_Ici_selfproof · cited by 34
- Ioi_mem_nhdsproof · cited by 27
Cited by9
Results whose statement or proof uses this declaration.
- BoundedVariationOn.tendsto_eVariationOn_Ico_zeroproof · cited by 3
- tendsto_atTop_of_mapClusterPtproof · cited by 3
- BoundedVariationOn.tendsto_eVariationOn_Icc_leftproof · cited by 2
- BoundedVariationOn.exists_tendsto_leftproof · cited by 2
- nhdsWithin_Ico_eq_nhdsLTproof · cited by 2
- BoundedVariationOn.tendsto_eVariationOn_Icc_zero_leftproof · cited by 1
- pi_Ici_mem_nhdsproof · cited by 1
- nhdsWithin_Icc_eq_nhdsLEproof · cited by 1
- eventually_ge_nhdsproof · cited by 1