Theorems · Theorem · functional analysis
NormedAddGroup.tendsto_nhds_zero
∀ {α : Type u_2} {E : Type u_5} [inst : SeminormedAddGroup E] {f : α → E} {l : Filter α},
Filter.Tendsto f l (nhds 0) ↔ ∀ ε > 0, ∀ᶠ (x : α) in l, ‖f x‖ < ε- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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 and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- nhdsstatement · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstostatement · cited by 3,814
- Filter.Eventuallystatement and proof · cited by 3,134
- SeminormedAddGroupstatement and proof · cited by 331
- dist_zero_rightproof · cited by 172
- Metric.tendsto_nhdsproof · cited by 20
Cited by6
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleO_iff_exists_eq_mulproof · cited by 3
- PadicInt.fwdDiff_tendsto_zeroproof · cited by 2
- tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_supportproof · cited by 1
- Filter.Tendsto.op_zero_isBoundedUnder_le'proof · cited by 1
- IsCompactOperator.antilipschitz_of_not_hasEigenvalueproof · cited by 1
- NormedAddCommGroup.tendsto_nhds_zeroproof · cited by 0