Theorems · Theorem · complex analysis

FormalMultilinearSeries.sum_mem

∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Semiring 𝕜] [inst_1 : AddCommMonoid E] [inst_2 : AddCommMonoid F]
  [inst_3 : Module 𝕜 E] [inst_4 : Module 𝕜 F] [inst_5 : TopologicalSpace E] [inst_6 : TopologicalSpace F]
  [inst_7 : ContinuousAdd E] [inst_8 : ContinuousAdd F] [inst_9 : ContinuousConstSMul 𝕜 E]
  [inst_10 : ContinuousConstSMul 𝕜 F] {S : Type u_6} {s : S} [inst_11 : SetLike S F] [AddSubmonoidClass S F],
  IsClosed ↑s → ∀ (p : FormalMultilinearSeries 𝕜 E F) (x : E), (∀ (k : ℕ), ((p k) fun x_1 => x) ∈ s) → p.sum x ∈ s

Defined in

Mathlib.Analysis.Analytic.ConvergenceRadius

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleTopologicalSpaceTopologicalSpaceContinuousAddContinuousAddContinuousConstSMulContinuousConstSMulSetLikeAddSubmonoidClass