Theorems · Theorem · general topology
left_nhdsWithin_Ioo_neBot
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α] {a b : α},
a < b → (nhdsWithin a (Set.Ioo a b)).NeBot- Defined in
- Mathlib.Topology.Order.DenselyOrdered
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- nhdsWithinstatement · cited by 1,912
- OrderTopologystatement and proof · cited by 1,355
- Set.Ioostatement · cited by 1,214
- Filter.NeBotstatement · cited by 853
- DenselyOrderedstatement and proof · cited by 471
- Set.nonempty_Iooproof · cited by 23
- isGLB_Iooproof · cited by 5
- IsGLB.nhdsWithin_neBotproof · cited by 2
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