Theorems · Theorem · general topology

SuccOrder.hasBasis_nhds_Ioc_of_exists_lt

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

Defined in

Mathlib.Topology.Order.Basic

Cited by

3 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologySuccOrder