For topologoical spaces (Τ1,X1) and (Τ2,X2),
{(G1 x G2)| G1 ∈ Τ1; G2 ∈ Τ2 is a base for the product topology T(X1 x X2)

We know:
B is a base for Τ iff
(1) B⊆Τ and,
(2) For every G∈Τ, if p∈G, then there is B∈B such that p∈B⊆G.