Does there exist a topology $\tau$ on $X \times Y$ such that $\Pi_x$ or $\Pi_y$ is not continuous where $\Pi_x$ is the projection of $X \times Y$ on $X$ and $\Pi_y$ is the projecion of $X \times Y$ on $Y$?
By the definition of product topology $\tau'$ on $X \times Y$ we see that it is the smallest topology on $X \times Y$ such that the projection map $\Pi_x , \Pi_y$ are continuous.
I have not come across any topology such that the projection maps are not continuous.Does there exists such a topology?