Theorems · Theorem · several complex variables

AnalyticOn.inv

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝕝 : Type u_8} [inst_3 : NormedDivisionRing 𝕝] [inst_4 : NormedAlgebra 𝕜 𝕝] {f : E → 𝕝}
  {s : Set E}, AnalyticOn 𝕜 f s → (∀ x ∈ s, f x ≠ 0) → AnalyticOn 𝕜 f⁻¹ s

(f x)⁻¹ is analytic away from f x = 0

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedDivisionRingNormedAlgebra