Theorems · Theorem · general topology
nhds_basis_Ioo_pos
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : AddCommGroup α] [inst_2 : LinearOrder α] [IsOrderedAddMonoid α]
[OrderTopology α] [NoMaxOrder α] (a : α), (nhds a).HasBasis (fun ε => 0 < ε) fun ε => Set.Ioo (a - ε) (a + ε)- Defined in
- Mathlib.Topology.Order.LeftRightNhds
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Filterproof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- OrderTopologystatement and proof · cited by 1,355
- Set.Ioostatement and proof · cited by 1,214
- Filter.HasBasisstatement and proof · cited by 604
Cited by4
Results whose statement or proof uses this declaration.
- Hyperreal.isSt_ofSeq_iff_tendstoproof · cited by 7
- AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilterproof · cited by 2
- nhds_basis_Icc_posproof · cited by 1
- nhds_basis_Ioo_pos_of_posproof · cited by 0