∀ {A : Type u_2} {B : Type u_3} {C : Type u_4} [inst : Monoid A] [inst_1 : Monoid B] [inst_2 : Monoid C]
  [inst_3 : TopologicalSpace A] [inst_4 : TopologicalSpace B] [inst_5 : TopologicalSpace C] (f : A →ₜ* B) (g : A →ₜ* C),
  f.prod g = { toMonoidHom := f.prod g.toMonoidHom, continuous_toFun := ⋯ }