Let $(X,\mathcal{T}_X)$ and $(Y,\mathcal{T}_Y)$ be \reftext{def:topological-space-2026a}{topological spaces}. The product topology on the \reftext{def:cartesian-product-sets-2026a}{Cartesian product} $X\times Y$ is the collection of all subsets $W\subseteq X\times Y$ with the following property:

for every point $(x,y)\in W$, there exist sets $U\in\mathcal{T}_X$ and $V\in\mathcal{T}_Y$ such that