Theorems · Theorem · general topology
Icc_mem_nhdsSet_Ioc
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderClosedTopology α] {a b c d : α},
a ≤ b → c < d → Set.Icc a d ∈ nhdsSet (Set.Ioc b c)- Defined in
- Mathlib.Topology.Order.NhdsSet
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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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.Iocstatement · cited by 971
- OrderClosedTopologystatement and proof · cited by 445
- nhdsSetstatement · cited by 267
- Filter.inter_memproof · cited by 153
- Ici_mem_nhdsSet_Iocproof · cited by 2
- Iic_mem_nhdsSet_Iocproof · cited by 2
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