Theorems · Theorem · general topology

Filter.Tendsto.finset_sup_nhds_apply

∀ {L : Type u_1} [inst : TopologicalSpace L] {ι : Type u_3} {α : Type u_4} {s : Finset ι} {f : ι → α → L} {l : Filter α}
  {g : ι → L} [inst_1 : SemilatticeSup L] [inst_2 : OrderBot L] [ContinuousSup L],
  (∀ i ∈ s, Filter.Tendsto (f i) l (nhds (g i))) → Filter.Tendsto (fun a => s.sup fun x => f x a) l (nhds (s.sup g))

Defined in

Mathlib.Topology.Order.Lattice

Cited by

3 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceSemilatticeSupOrderBotContinuousSup