Theorems · Theorem · functional analysis
NormedAddCommGroup.tendsto_nhds_nhds
∀ {E : Type u_5} {F : Type u_6} [inst : SeminormedAddCommGroup E] [inst_1 : SeminormedAddCommGroup F] {f : E → F}
{x : E} {y : F}, Filter.Tendsto f (nhds x) (nhds y) ↔ ∀ ε > 0, ∃ δ > 0, ∀ (x' : E), ‖x' - x‖ < δ → ‖f x' - y‖ < ε- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_neg_addproof · cited by 12
- NormedAddGroup.tendsto_nhds_nhdsproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MultilinearMap.exists_bound_of_continuousproof · cited by 2