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Theorems · Theorem · general topology

PredOrder.hasBasis_nhds_Ioc_of_exists_gt

Deprecated since 2026-04-19Use PredOrder.hasBasis_nhds_Ico_of_exists_gt instead.

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [PredOrder α] {a : α},
  (∃ l, a < l) → (nhds a).HasBasis (fun x => a < x) fun x => Set.Ico a x

Alias of PredOrder.hasBasis_nhds_Ico_of_exists_gt.

Defined in
Mathlib.Topology.Order.Basic
Cited by
0 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceLinearOrderOrderTopologyPredOrder
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TopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrdernhds · cited by 5554nhdsOrderTopology · cited by 1355OrderTopologySet.Ico · cited by 799Set.IcoFilter.HasBasis · cited by 604Filter.HasBasisPredOrder · cited by 334PredOrderPredOrder.hasBasis_nhds_Ico_of_exists_gt · cited by 4PredOrder.hasBasis_nhds_I…PredOrder.hasBasis_nhds_Ioc_o…CITED BYCITES

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