Theorems · Theorem · general topology

nhds_basis_Icc_pos

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : AddCommGroup α] [inst_2 : LinearOrder α] [IsOrderedAddMonoid α]
  [OrderTopology α] [NoMaxOrder α] [DenselyOrdered α] (a : α),
  (nhds a).HasBasis (fun x => 0 < x) fun ε => Set.Icc (a - ε) (a + ε)

Defined in

Mathlib.Topology.Order.LeftRightNhds

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupLinearOrderIsOrderedAddMonoidOrderTopologyNoMaxOrderDenselyOrdered