Theorems · Theorem · general topology
EMetric.tendsto_atTop
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [Nonempty β] [inst_2 : SemilatticeSup β] {u : β → α} {a : α},
Filter.Tendsto u Filter.atTop (nhds a) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, edist (u n) a < ε- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- PseudoEMetricSpacestatement and proof · cited by 1,536
- SemilatticeSupstatement and proof · cited by 785
- EDist.ediststatement and proof · cited by 735
- Filter.HasBasis.tendsto_iffproof · cited by 60
- Filter.atTop_basisproof · cited by 42
- Metric.nhds_basis_eballproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.TendstoInMeasure.exists_seq_tendsto_aeproof · cited by 5