Let $(X,\tau_X)$ and $(Y,\tau_Y)$ be [topological spaces](/page/Topological%20Space), and let $\tau_X \times \tau_Y$ denote the [product topology](/page/Product%20Topology) on $X \times Y$. Assume that $Y \neq \varnothing$. If $(X,\tau_X)$ is disconnected, then $X \times Y$ is disconnected with respect to $\tau_X \times \tau_Y$.