Theorems · Theorem · general topology

Filter.Tendsto.partialSups_apply

∀ {L : Type u_1} [inst : SemilatticeSup L] [inst_1 : TopologicalSpace L] [ContinuousSup L] {α : Type u_2} {l : Filter α}
  {f : ℕ → α → L} {g : ℕ → L} {n : ℕ},
  (∀ k ≤ n, Filter.Tendsto (f k) l (nhds (g k))) →
    Filter.Tendsto (fun a => (partialSups fun x => f x a) n) l (nhds ((partialSups g) n))

Defined in

Mathlib.Topology.Order.PartialSups

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupTopologicalSpaceContinuousSup