Theorems · Theorem · general topology
limsSup_nhds
∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α] (a : α),
(nhds a).limsSup = a- Defined in
- Mathlib.Topology.Order.LiminfLimsup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 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
- Set.ofPredproof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- OrderTopologystatement and proof · cited by 1,355
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- mem_of_mem_nhdsproof · cited by 126
- gt_mem_nhdsproof · cited by 37
- Filter.limsSupstatement · cited by 29
- Filter.sets_of_supersetproof · cited by 14
- ge_mem_nhdsproof · cited by 8
- isBounded_le_nhdsproof · cited by 4
- csInf_eq_of_forall_ge_of_forall_gt_exists_ltproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- limsInf_eq_of_le_nhdsproof · cited by 2
- limsInf_nhdsproof · cited by 1