# Category:Product Spaces

This category contains results about Product Spaces in the context of Topology.

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 Tychonoff topology on $S_1 \times S_2$.

From Natural Basis of Tychonoff Topology of Finite Product, $\tau$ is the topology generated by the basis

$\BB = \set{U_1 \times U_2: U_1 \in \tau_1, U_2 \in \tau_2}$.

The topological space $\struct{S_1 \times S_2, \tau}$ is called the product space of $\struct{S_1, \tau_1}$ and $\struct{S_2, \tau_2}$.