\begin{definition}[Definition:Product Topology/Two Factor Spaces]
Let $\struct {S_1, \tau_1}$ and $\struct {S_2, \tau_2}$ be topological spaces.
Let $S_1 \times S_2$ be the cartesian product of $S_1$ and $S_2$.
The '''product topology''' $\tau$ on $S_1 \times S_2$ is the topology generated by the natural basis:
:$\BB = \set {U_1 \times U_2: U_1 \in \tau_1, U_2 \in \tau_2}$
\end{definition}