∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s t : Set α} {f : α → β},
  IsOpen s → IsOpen t → (ContinuousOn f (s ∪ t) ↔ ContinuousOn f s ∧ ContinuousOn f t)