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Found problems: 1

2006 Miklós Schweitzer, 9
Does the circle T = R / Z have a self-homeomorphism $\phi$ that is singular (that is, its derivative is almost everywhere 0), but the mapping $f:T \to T$ , $f(x) = \phi^{-1} (2\phi(x))$ is absolutely continuous?
homeomorphism topology absolute continuity calculus geometry