∀ {X : Type u} {ι : Type u_5} {A : ι → Type u_6} [inst : TopologicalSpace X] [T : (i : ι) → TopologicalSpace (A i)]
  {f : X → (i : ι) → A i} {x : X}, ContinuousAt f x ↔ ∀ (i : ι), ContinuousAt (fun y => f y i) x