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

Lemma Rmult_continuous_at_origin: continuous_at_2arg Rmult 0 0 (X:=RTop) (Y:=RTop) (Z:=RTop).