Theorems · Theorem · order theory
tendsto_ratCast_atTop_iff
∀ {α : Type u_1} {R : Type u_2} [inst : Field R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] [Archimedean R]
{f : α → ℚ} {l : Filter α}, Filter.Tendsto (fun n => ↑(f n)) l Filter.atTop ↔ Filter.Tendsto f l Filter.atTop- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement and proof · cited by 8,121
- Fieldstatement and proof · cited by 7,404
- Filter.Tendstostatement and proof · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement and proof · cited by 2,405
- Archimedeanstatement and proof · cited by 603
- Filter.tendsto_comap_iffproof · cited by 55
- Rat.comap_cast_atTopproof · cited by 2
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