(* Ropp_continuous was already proved in RTopology *)

Corollary quotient_continuous: forall (X:TopologicalSpace)
(f g:point_set X -> point_set RTop) (x0:point_set X),
continuous_at f x0 -> continuous_at g x0 -> g x0 <> 0 ->
continuous_at (fun x:point_set X => f x / g x) x0 (Y:=RTop).