Theorems · Theorem · functional analysis
NormedGroup.tendsto_nhds_nhds
∀ {E : Type u_5} {F : Type u_6} [inst : SeminormedGroup E] [inst_1 : SeminormedGroup F] {f : E → F} {x : E} {y : F},
Filter.Tendsto f (nhds x) (nhds y) ↔ ∀ ε > 0, ∃ δ > 0, ∀ (x' : E), ‖x'⁻¹ * x‖ < δ → ‖(f x')⁻¹ * 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.
Cites6
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
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstostatement · cited by 3,814
- SeminormedGroupstatement and proof · cited by 250
- dist_eq_norm_inv_mulproof · cited by 41
Cited by1
Results whose statement or proof uses this declaration.
- NormedCommGroup.tendsto_nhds_nhdsproof · cited by 0