Theorems · Theorem · general topology
exists_seq_tendsto_limsSup
∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
[FirstCountableTopology α] {f : Filter α} [f.NeBot] [f.IsCountablyGenerated],
autoParam (Filter.IsCobounded (fun x1 x2 => x1 ≤ x2) f) exists_seq_tendsto_limsSup._auto_1 →
autoParam (Filter.IsBounded (fun x1 x2 => x1 ≤ x2) f) exists_seq_tendsto_limsSup._auto_3 →
∃ x, Filter.Tendsto x Filter.atTop (nhds f.limsSup) ∧ Filter.Tendsto x Filter.atTop f- Defined in
- Mathlib.Topology.Order.LiminfLimsup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
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
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- OrderTopologystatement and proof · cited by 1,355
- Filter.NeBotstatement and proof · cited by 853
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- FirstCountableTopologystatement and proof · cited by 106
- Filter.IsBoundedstatement and proof · cited by 45
- Filter.IsCoboundedstatement and proof · cited by 42
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