There is a theorem that says that if $f\colon X \rightarrow Y$ is bijective and continuous, then $f$ is an homeomorphism if $X$ is compact and $Y$ is Hausdorff.
What about if $X$ is Hausdorff and $Y$ is compact?
My question arises because I have noted that there a some kind of dual relations between compact and Hausdorff spaces. In this specific problem, I think that it must be false, but I can´t give any counterexample.
Thanks in advance.