Theorems · Theorem · functional analysis
SeminormedGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_one
∀ {ι : Type u_2} {κ : Type u_3} {G : Type u_6} [inst : SeminormedGroup G] {f : ι → κ → G} {s : Set κ} {l : Filter ι},
UniformCauchySeqOn f l s ↔ TendstoUniformlyOn (fun n z => (f n.1 z)⁻¹ * f n.2 z) 1 (l ×ˢ l) s- 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
- SeminormedGroup
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Cites11
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- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- SProd.sprodstatement and proof · cited by 1,750
- Filter.principalproof · cited by 740
- SeminormedGroupstatement and proof · cited by 250
- TendstoUniformlyOnstatement · cited by 129
- TendstoUniformlyOnFilterproof · cited by 50
- UniformCauchySeqOnstatement and proof · cited by 33
- tendstoUniformlyOn_iff_tendstoUniformlyOnFilterproof · cited by 13
- uniformCauchySeqOn_iff_uniformCauchySeqOnFilterproof · cited by 6
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