Definition WeakTopology1 := WeakTopology (True_rect f).

(* Specifications: *)
Lemma weak_topology1_topology: forall U:Ensemble X, @open WeakTopology1 U -> exists V:Ensemble (point_set Y), open V /\ U = inverse_image f V.
Lemma weak_topology1_makes_continuous_func: continuous f (X:=WeakTopology1).