Theorems · Theorem · functional analysis
NormedCommGroup.tendsto_nhds_nhds
∀ {E : Type u_5} {F : Type u_6} [inst : SeminormedCommGroup E] [inst_1 : SeminormedCommGroup 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
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- SeminormedCommGroupstatement and proof · cited by 191
- norm_inv_mulproof · cited by 5
- NormedGroup.tendsto_nhds_nhdsproof · cited by 1
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