Theorems · Theorem · general topology
Metric.tendsto_atTop
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [Nonempty β] [inst_2 : SemilatticeSup β] {u : β → α} {a : α},
Filter.Tendsto u Filter.atTop (nhds a) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, dist (u n) a < ε- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 115 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.
- Realstatement and proof · cited by 25,697
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- SemilatticeSupstatement and proof · cited by 785
- Filter.HasBasis.tendsto_iffproof · cited by 60
- Filter.atTop_basisproof · cited by 42
- Metric.nhds_basis_ballproof · cited by 41
Cited by10
Results whose statement or proof uses this declaration.
- cauchySeq_iff_le_tendsto_0proof · cited by 5
- EulerProduct.eulerProduct_hasProdproof · cited by 4
- Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSetproof · cited by 2
- MeasureTheory.isTightMeasureSet_of_tendsto_charFunproof · cited by 1
- tendsto_tsum_div_pow_atTop_integralproof · cited by 1
- MeasureTheory.Measure.MeasureDense.of_generateFrom_isSetAlgebra_finiteproof · cited by 1
- AbsoluteValue.denseRange_algebraMap_piproof · cited by 1
- tendsto_smoothingFun_of_ne_zeroproof · cited by 1
- GromovHausdorff.totallyBoundedproof · cited by 0