In part a of a question, I proved that if a topological space $X$ is compact, and a topological space $Y$ is Hausdorff, then any continuous bijection $f: X \rightarrow Y$ is a homeomorphism.
The part b says this: We have seen that the compactness of $X$ is necessary in order for the conclusion of a to be true. Show that the condition that $Y$ be Hausdorff is necessary as well.
Now, I have no worldly clue what the question is asking me to do. I suspect that the question is asking me to show that if $f: X \rightarrow Y$ is a homeomorphism where $Y$ is Hausdorff, then $X$ is Hausdorff as well. Which is something I can prove easily. But I don't think the language translates to this question. Can I get some help?
Full disclosure - this is an assignment question. And I'm not looking for any kind of a solution to any question that I have written. Just clarification. Thanks!