\begin{definition}[Definition:Product Space (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 $S_2$.
Let $\tau$ be the product topology on $S_1 \times S_2$.
The topological space $\struct {S_1 \times S_2, \tau}$ is called  the '''product space''' of $\struct {S_1, \tau_1}$ and $\struct {S_2, \tau_2}$.
\end{definition}