Theorems · Theorem · complex analysis

MeromorphicOn.meromorphicOrderAt_ne_top_of_isPreconnected

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜} {U : Set 𝕜},
  MeromorphicOn f U →
    ∀ {y : 𝕜}, IsPreconnected U → x ∈ U → y ∈ U → meromorphicOrderAt f x ≠ ⊤ → meromorphicOrderAt f y ≠ ⊤

On a preconnected set, a meromorphic function has finite order at one point if it has finite order at another point.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

0 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace