Definition ProductTopology2 : TopologicalSpace :=
  WeakTopology prod2_proj.

(* Specifications: *)
Lemma prod2_conv1_cont: continuous prod2_conv1 (Y:=ProductTopology2).
Lemma prod2_conv2_cont: continuous prod2_conv2 (X:=ProductTopology2).
Lemma product2_fst_continuous: continuous (@fst (point_set X) (point_set Y)) (X:=ProductTopology2).
Lemma product2_snd_continuous: continuous (@snd (point_set X) (point_set Y)) (X:=ProductTopology2).
Lemma product2_map_continuous: forall (W:TopologicalSpace) (f:point_set W -> point_set X) (g:point_set W -> point_set Y) (w:point_set W), continuous_at f w -> continuous_at g w -> continuous_at (fun w:point_set W => (f w, g w)) w (Y:=ProductTopology2).
Lemma ProductTopology2_basis_is_basis: open_basis ProductTopology2_basis.