Theorems · Theorem · commutative algebra

PowerSeries.WithPiTopology.summable_of_tendsto_order_atTop_nhds_top

∀ (R : Type u_1) [inst : TopologicalSpace R] [inst_1 : Semiring R] {ι : Type u_2} {f : ι → PowerSeries R}
  [inst_2 : LinearOrder ι] [LocallyFiniteOrderBot ι],
  Filter.Tendsto (fun i => (f i).order) Filter.atTop (nhds ⊤) → Summable f

A family of PowerSeries is summable if their order tends to infinity.

Defined in

Mathlib.RingTheory.PowerSeries.PiTopology

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceSemiringLinearOrderLocallyFiniteOrderBot