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).

Lemma open_interval_homeomorphic_to_real_line: let U:=characteristic_function_to_ensemble (fun x:point_set RTop => -1 < x < 1) in homeomorphic RTop (SubspaceTopology U).