Theorems · Theorem · several complex variables

isOpen_analyticAt

∀ (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] [CompleteSpace F] (f : E → F),
  IsOpen {x | AnalyticAt 𝕜 f x}

For any function f from a normed vector space to a Banach space, the set of points x such that f is analytic at x is open.

Defined in

Mathlib.Analysis.Analytic.ChangeOrigin

Cited by

6 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace