∀ {F : Type u_1} {X : Type u_2} {Y : Type u_3} {Z : Type u_4} [inst : FunLike F X Y] [inst_1 : TopologicalSpace F]
  [inst_2 : TopologicalSpace X] [inst_3 : TopologicalSpace Y] [ContinuousEval F X Y] [inst_5 : TopologicalSpace Z]
  {f : Z → F} {g : Z → X}, Continuous f → Continuous g → Continuous fun z => (f z) (g z)