Theorems · Theorem · functional analysis
NormedAddCommGroup.tendsto_nhds_zero
Deprecated since 2026-02-17Use NormedAddGroup.tendsto_nhds_zero instead.
∀ {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‖ < εAlias of NormedAddGroup.tendsto_nhds_zero.
- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Norm.normstatement · cited by 5,413
- Filter.Tendstostatement · cited by 3,814
- Filter.Eventuallystatement · cited by 3,134
- SeminormedAddGroupstatement · cited by 331
- NormedAddGroup.tendsto_nhds_zeroproof · cited by 6
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