\b[False.] Take $X=[0,1]$, $Y=S^1$ and the <surjection> $f(t)=e^{2\pi it}$. The interval is <compact> and <connected>, and the circle is <Hausdorff>. But $f^{-1}(1)=\{0,1\}$ is a disconnected two-point subspace. Thus a continuous <surjection> need not have connected fibers.

Solution

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

 Solution (source code)