Theorems · Theorem · general topology

Filter.tendsto_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {f : (i : ι) → Filter (α i)} {β : Type u_3} {m : β → (i : ι) → α i} {l : Filter β},
  Filter.Tendsto m l (Filter.pi f) ↔ ∀ (i : ι), Filter.Tendsto (fun x => m x i) l (f i)

Defined in

Mathlib.Order.Filter.Pi

Cited by

7 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound