Theorems · Theorem · general topology
Filter.exists_seq_tendsto
∀ {α : Type u_1} (f : Filter α) [f.IsCountablyGenerated] [f.NeBot], ∃ x, Filter.Tendsto x Filter.atTop fIf f is a nontrivial countably generated filter, then there exists a sequence that converges
to f.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- Filter.NeBotstatement and proof · cited by 853
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- Filter.HasAntitoneBasisproof · cited by 43
- Filter.nonempty_of_memproof · cited by 36
- Filter.exists_antitone_basisproof · cited by 10
- Filter.HasAntitoneBasis.memproof · cited by 6
- Filter.HasAntitoneBasis.tendstoproof · cited by 2
Cited by21
Results whose statement or proof uses this declaration.
- stronglyMeasurable_of_tendstoproof · cited by 12
- aestronglyMeasurable_of_tendsto_aeproof · cited by 9
- aemeasurable_of_tendsto_metrizable_aeproof · cited by 7
- Filter.tendsto_iff_seq_tendstoproof · cited by 5
- ENNReal.measurable_of_tendsto'proof · cited by 4
- Filter.exists_seq_monotone_tendsto_atTop_atTopproof · cited by 3
- MeasureTheory.Lp.eLpNorm_le_of_ae_tendstoproof · cited by 3
- isCountablyCompact_iff_seq_clusterPtproof · cited by 2
- ClusterPt.exists_seq_tendstoproof · cited by 2
- Bornology.IsVonNBounded.extend_scalarsproof · cited by 2
- measurableSet_bddAbove_rangeproof · cited by 2
- MeasureTheory.measurable_stoppedValueproof · cited by 2