Theorems · Theorem · general topology
Metric.tendsto_nhds
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] {f : Filter β} {u : β → α} {a : α},
Filter.Tendsto u f (nhds a) ↔ ∀ ε > 0, ∀ᶠ (x : β) in f, dist (u x) a < ε- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.Eventuallystatement · cited by 3,134
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- Filter.HasBasis.tendsto_right_iffproof · cited by 81
- Metric.nhds_basis_ballproof · cited by 41
Cited by20
Results whose statement or proof uses this declaration.
- NormedAddGroup.tendsto_nhds_zeroproof · cited by 6
- Metric.continuousAt_iff'proof · cited by 5
- tendsto_integral_exp_inner_smul_cocompactproof · cited by 3
- IsUnifLocDoublingMeasure.tendsto_closedBall_filterAtproof · cited by 3
- tendsto_tsum_of_dominated_convergenceproof · cited by 2
- Frullani.tendsto_integral_inv_smul_of_tendsto_uniformproof · cited by 2
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- BoundedContinuousFunction.tendsto_iff_tendstoUniformlyproof · cited by 2
- hasFDerivAt_of_tendstoUniformlyOnFilterproof · cited by 2
- NormedGroup.tendsto_nhds_oneproof · cited by 2
- lp.hasSum_singleproof · cited by 2
- HasFPowerSeriesWithinOnBall.tendsto_partialSum_prodproof · cited by 2