∀ {R : Type u_4} [inst : CommSemiring R] {A : Type u_1} [inst_1 : Semiring A] [inst_2 : TopologicalSpace A]
  {B : Type u_3} [inst_3 : Semiring B] [inst_4 : TopologicalSpace B] [inst_5 : Algebra R A] [inst_6 : Algebra R B]
  {C : Type u_2} [inst_7 : Semiring C] [inst_8 : Algebra R C] [inst_9 : TopologicalSpace C] (g : B →A[R] C)
  (f : A →A[R] B), Continuous ((↑↑g.toRingHom).toFun ∘ ⇑↑↑f)