Theorems · Theorem · general topology
Iic_mem_nhdsSet_Icc
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderClosedTopology α] {a b c : α},
b < c → Set.Iic c ∈ nhdsSet (Set.Icc a b)- Defined in
- Mathlib.Topology.Order.NhdsSet
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 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.Iccstatement · cited by 1,702
- Set.Iicstatement · cited by 1,111
- OrderClosedTopologystatement and proof · cited by 445
- Filter.mem_of_supersetproof · cited by 308
- nhdsSetstatement · cited by 267
- Set.Iio_subset_Iic_selfproof · cited by 21
- Iio_mem_nhdsSet_Iccproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Iic_mem_nhdsSet_Iocproof · cited by 2
- Ioc_mem_nhdsSet_Iccproof · cited by 0
- Icc_mem_nhdsSet_Iccproof · cited by 0