Theorems · Theorem · general topology
IsLUB.frequently_mem
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] {a : α} {s : Set α},
IsLUB s a → s.Nonempty → ∃ᶠ (x : α) in nhdsWithin a (Set.Iic a), x ∈ s- Defined in
- Mathlib.Topology.Order.IsLUB
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- Set.Nonemptystatement and proof · cited by 2,627
- nhdsWithinstatement and proof · cited by 1,912
- le_rflproof · cited by 1,558
- OrderTopologystatement and proof · cited by 1,355
- Set.Iioproof · cited by 1,166
- Set.Iicstatement and proof · cited by 1,111
- Set.Iocproof · cited by 971
Cited by3
Results whose statement or proof uses this declaration.
- IsLUB.exists_seq_strictMono_tendsto_of_notMemproof · cited by 4
- IsGLB.frequently_memproof · cited by 1
- IsLUB.frequently_nhds_memproof · cited by 1