Theorems · Theorem · general topology
Ico_mem_nhds
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderClosedTopology α] {a b x : α},
b < x → x < a → Set.Ico b a ∈ nhds x- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, 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.Icostatement · cited by 799
- OrderClosedTopologystatement and proof · cited by 445
- Filter.mem_of_supersetproof · cited by 308
- Set.Ioo_subset_Ico_selfproof · cited by 29
- Ioo_mem_nhdsproof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- continuousAt_fractproof · cited by 1
- pi_Ico_mem_nhdsproof · cited by 1
- ConvexOn.continuousOn_Iccproof · cited by 1