We know that for any two topological spaces $X(\ne\emptyset)$ and $Y(\ne\emptyset)$, there exists an open, continuous and surjective map $\pi:X\times Y\to X$ defined by $\pi(x,y)=x$ for all $(x,y)\in X\times Y$ where the topology on $X\times Y$ is the product topology.
My question is,
Let $X(\ne\emptyset)$ and $Y(\ne\emptyset)$ be two topological spaces and $X\times Y$ is given the the product topology. Does there always exist a closed, continuous and surjective map $\Psi:X\times Y\to X$? If so then can anyone give an explicit example?