I am trying to learn topology but I dont know how to proof this problem.
Let $X$ be a Hausdorff space, ~ an equivalence relation and $\pi:X \to X/{\sim}$ the canonical map. $X/{\sim}$ is also Hausdorff, if there exists a continuous function $s:X/{\sim} \to X$, such that $\pi \circ s=\textrm{Id}_{X/{\sim}}$
I've read that the diagonal of a Hausdorff space is closed regarding the product topology but I don't know how to proceed or where to start