∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] [inst_3 : TopologicalSpace δ] {f : α → γ} {g : β → δ} {s : Set α} {t : Set β},
  ContinuousOn f s → ContinuousOn g t → ContinuousOn (Prod.map f g) (s ×ˢ t)