Theorems · Theorem · real analysis
Polynomial.abs_tendsto_atTop
∀ {𝕜 : Type u_1} [inst : NormedField 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] (P : Polynomial 𝕜)
[OrderTopology 𝕜], 0 < P.degree → Filter.Tendsto (fun x => |Polynomial.eval x P|) Filter.atTop Filter.atTop- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Polynomialstatement and proof · cited by 5,681
- Filter.Tendstostatement · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement · cited by 2,405
- absstatement · cited by 1,814
- WithBotstatement · cited by 1,498
- OrderTopologystatement and proof · cited by 1,355
- NormedFieldstatement and proof · cited by 1,084
- Polynomial.evalstatement · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Filter.Tendsto.compproof · cited by 560
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.isBoundedUnder_abs_atTop_iffproof · cited by 2
- Polynomial.abs_tendsto_atBotproof · cited by 2
- Polynomial.abs_tendsto_atTop_iffproof · cited by 0