Let $(X,\mathcal{T}_X)$ and $(Y,\mathcal{T}_Y)$ be \reftext{def:topological-space-2026a}{topological spaces}. Suppose that both $X$ and $Y$ are \reftext{def:compact-space-and-subset-2026a}{compact}. Then $X\times Y$ is compact when equipped with the \reftext{def:product-topology-2026a}{product topology}.