Corollary product_continuous: forall (X:TopologicalSpace)
  (f g:point_set X -> point_set RTop) (x:point_set X),
  continuous_at f x -> continuous_at g x ->
  continuous_at (fun x:point_set X => f x * g x) x (Y:=RTop).

(* Specifications: *)
Lemma Rinv_continuous_at_1: continuous_at Rinv 1 (X:=RTop) (Y:=RTop).
Lemma Rinv_continuous: forall x0:R, x0<>0 -> continuous_at Rinv x0 (X:=RTop) (Y:=RTop).
Lemma Rdiv_continuous: forall x y:R, y <> 0 -> continuous_at_2arg Rdiv x y (X:=RTop) (Y:=RTop) (Z:=RTop).