Theorems · Theorem · complex analysis

AnalyticWithinAt.exists_mem_nhdsWithin_analyticOn

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {F : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] [CompleteSpace F] {f : E → F}
  {s : Set E} {x : E}, AnalyticWithinAt 𝕜 f s x → ∃ u ∈ nhdsWithin x (insert x s), AnalyticOn 𝕜 f u

Defined in

Mathlib.Analysis.Analytic.Within

Cited by

0 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace