Theorems · Theorem · functional analysis
SeminormedAddGroup.tendstoUniformlyOn_zero
∀ {ι : Type u_2} {κ : Type u_3} {G : Type u_6} [inst : SeminormedAddGroup G] {f : ι → κ → G} {s : Set κ} {l : Filter ι},
TendstoUniformlyOn f 0 l s ↔ ∀ ε > 0, ∀ᶠ (i : ι) in l, ∀ x ∈ s, ‖f i x‖ < ε- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement and proof · cited by 3,134
- SeminormedAddGroupstatement and proof · cited by 331
- TendstoUniformlyOnstatement · cited by 129
- dist_zero_leftproof · cited by 15
- Metric.tendstoUniformlyOn_iffproof · cited by 14
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