Inductive ProductTopology2_basis :
Family (point_set ProductTopology2) :=
| intro_product2_basis_elt:
forall (U:Ensemble (point_set X))
(V:Ensemble (point_set Y)),
open U -> open V ->
In ProductTopology2_basis
[ p:point_set ProductTopology2 |
let (x,y):=p in (In U x /\ In V y) ].

Lemma ProductTopology2_basis_is_basis:
open_basis ProductTopology2_basis.