If $X$ is Hausdorff and $\sim$ is an equivalence relation in $X$, then $X/\sim$ endowed with the quotient topology is also Hausdorff
To make this problem I am using the following post:
So, I would say that this is false since the equivalence relation must be closed, how can I find a counterexample of this? Could anyone help me please? Where where $X$ is Haudorff but $X/\sim$ is not. Thank you very much.