Theorems · Theorem · general topology
nhdsLE_basis_of_exists_lt
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] {a : α},
(∃ u, u < a) → (nhdsWithin a (Set.Iic a)).HasBasis (fun u => u < a) fun u => Set.Ioc u a- Defined in
- Mathlib.Topology.Order.Basic
- Cited by
- 5 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.
Cites13
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
- OrderTopologystatement and proof · cited by 1,355
- Set.Iicstatement · cited by 1,111
- Set.Iocstatement · cited by 971
- Filter.HasBasisstatement · cited by 604
- le_max_leftproof · cited by 215
- le_max_rightproof · cited by 205
- max_ltproof · cited by 42
- Set.Ioc_subset_Ioc_leftproof · cited by 6
- Filter.hasBasis_biInf_principalproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- exists_Ioc_subset_of_mem_nhdsproof · cited by 8
- nhds_top_basisproof · cited by 5
- SuccOrder.hasBasis_nhds_Ioc_of_exists_ltproof · cited by 3
- exists_Icc_mem_subset_of_mem_nhdsLEproof · cited by 1
- nhdsLE_basisproof · cited by 0