Theorems · Theorem · general topology
nhdsGE_basis_Icc
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [NoMaxOrder α]
[DenselyOrdered α] {a : α}, (nhdsWithin a (Set.Ici a)).HasBasis (fun x => a < x) (Set.Icc a)The filter of right neighborhoods has a basis of closed intervals.
- Defined in
- Mathlib.Topology.Order.LeftRightNhds
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Set.Iccstatement · cited by 1,702
- OrderTopologystatement and proof · cited by 1,355
- Set.Icistatement · cited by 1,070
- Filter.HasBasisstatement · cited by 604
- DenselyOrderedstatement and proof · cited by 471
- NoMaxOrderstatement and proof · cited by 340
- exists_betweenproof · cited by 102
- Set.Ico_subset_Icc_selfproof · cited by 41
- Filter.HasBasis.to_hasBasisproof · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- mem_nhdsGE_iff_exists_Icc_subsetproof · cited by 1
- tendsto_gauge_nhds_zero_nhdsGEproof · cited by 1