Help me please to solve this problem. Let's $f : X \to Y$ be one-to-one and onto, prove that:
a) If $f : X\to Y $ a continuous function and $Y$ is Hausdorff then $X$ is Hausdorff.
b) If $f$ is open or closed and $X$ is Hausdorff then $Y$ is Hausdorff.
Thanks!