# Category:Product Spaces

Let $T_1 = \left({S_1, \tau_1}\right)$ and $T_2 = \left({S_2, \tau_2}\right)$ be topological spaces.
Let $S_1 \times S_2$ be the cartesian product of $S_1$ and $S_2$.
The product topology $\tau$ for $S_1 \times S_2$ is the topology with basis $\mathcal B = \left\{{U_1 \times U_2: U_1 \in \tau_1, U_2 \in \tau_2}\right\}$.