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- W3098001327 abstract "The Hausdorff dimension of a product can be strictly greater than that of , even when the Hausdorff dimension of is But when is countable, the Hausdorff dimensions of and are the same. Diagonalizations of covers define a natural hierarchy of properties which are weaker than countable and stronger than having Hausdorff dimension zero. Fremlin asked whether it is enough for to have the strongest property in this hierarchy (namely, being a -set) in order to assure that the Hausdorff dimensions of and are the same. We give a negative answer: Assuming the Continuum Hypothesis, there exists a -set and a set with Hausdorff dimension zero, such that the Hausdorff dimension of (a Lipschitz image of ) is maximal, that is, . However, we show that for the notion of a strong -set the answer is positive. Some related problems remain open." @default.
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- W3098001327 date "2003-10-29" @default.
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- W3098001327 title "Topological diagonalizations and Hausdorff dimension" @default.
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