Show that a continuous bijection $f : X \to Y$ with $X$ compact and $Y$ Hausdorff is a homeomorphism. Give an example to show that such a continuous bijection is not necessarily a homeomorphism if $Y$ is not assumed to be Hausdorff.
I'm having some trouble with the counterexample.
Would an $X$ interval in $\mathbb R$ and a $Y = S^1$ work?