Basis_for_Topology_on_Cartesian_Product

Let $T_1 = \struct{A_1, \tau_1}$ and $T_2 = \struct{A_2, \tau_2}$ be topological spaces. Let $A_1 \times A_2$ be the Cartesian product of $A_1$ and $A_2$. Let $\PP = \set{ U_1 \times U_2 : U_1 \in \tau_1, U_2 \in \tau_2}$ Then $\PP$ is a synthetic basis on $A_1 \times A_2$.