Theorems · Theorem · complex analysis

MeromorphicOn.analyticAt_mem_codiscreteWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜},
  MeromorphicOn f U → {x | AnalyticAt 𝕜 f x} ∈ Filter.codiscreteWithin U

Meromorphic functions on U are analytic on U, outside of a discrete subset.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

7 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace