Theorems · Theorem · several complex variables

CPolynomialAt.exists_ball_cpolynomialOn

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E},
  CPolynomialAt 𝕜 f x → ∃ r, 0 < r ∧ CPolynomialOn 𝕜 f (Metric.ball x r)

If f is continuously polynomial at a point, then it is continuously polynomial in a nonempty ball around that point.

Defined in

Mathlib.Analysis.Analytic.CPolynomialDef

Cited by

0 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace