Theorems · Theorem · several complex variables

AnalyticWithinAt.prod

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} {G : Type u_5}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {e : E} {f : E → F} {g : E → G} {s : Set E},
  AnalyticWithinAt 𝕜 f s e → AnalyticWithinAt 𝕜 g s e → AnalyticWithinAt 𝕜 (fun x => (f x, g x)) s e

The Cartesian product of analytic functions is analytic.

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

3 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace