∀ {ι : Type u_5} {A : ι → Type u_6} [T : (i : ι) → TopologicalSpace (A i)] {X : ι → Type u_9}
  [inst : (i : ι) → TopologicalSpace (X i)] {g : (i : ι) → A i → X i},
  (∀ (i : ι), Continuous (g i)) → Continuous fun f i => g i (f i)