Theorems · Theorem · general topology
Iic_mem_nhds
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a b : α},
b < a → Set.Iic a ∈ nhds b- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 6 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.Iicstatement · cited by 1,111
- Filter.mem_of_supersetproof · cited by 308
- ClosedIciTopologystatement and proof · cited by 156
- Iio_mem_nhdsproof · cited by 34
- Set.Iio_subset_Iic_selfproof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- eventually_le_nhdsproof · cited by 8
- nhdsWithin_Icc_eq_nhdsGEproof · cited by 5
- eventually_closedBall_subsetproof · cited by 3
- nhdsWithin_Ioc_eq_nhdsGTproof · cited by 3
- eVariationOn.eVariationOn_Ioc_eq_Icc_of_continuousWithinAt'proof · cited by 2
- pi_Iic_mem_nhdsproof · cited by 1