Theorems · Theorem · complex analysis
AnalyticOnNhd.eval_polynomial
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {A : Type u_5} [inst_1 : NormedCommRing A]
[inst_2 : NormedAlgebra 𝕜 A] (p : Polynomial A), AnalyticOnNhd 𝕜 (fun x => Polynomial.eval x p) Set.univ- Defined in
- Mathlib.Analysis.Analytic.Polynomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Polynomialstatement and proof · cited by 5,681
- Set.univstatement · cited by 3,945
- NormedAlgebrastatement and proof · cited by 1,165
- Polynomial.evalstatement · cited by 796
- NormedCommRingstatement and proof · cited by 218
- AnalyticOnNhdstatement · cited by 206
- analyticOnNhd_idproof · cited by 5
- AnalyticOnNhd.aeval_polynomialproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.C_eq_or_isOpenQuotientMap_evalproof · cited by 1