Require Export RTopology ProductTopology Homeomorphisms.
(* Ropp_continuous was already proved in RTopology *)

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).