\b[True.] The <Hausdorff> assumption makes $\{y\}$ closed in $Y$. Its <inverse image> under the <continuous map> $f$ is closed in the <compact space> $X$, and a <closed subset of a compact space> is compact. This is the <compactness> of the fiber with its <subspace topology>.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / E / 3 / c / Solution

 Solution (source code)