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The Continuum Hypothesis implies an Erdö-Sierpiński like duality between the ideal of first category subsets of ℝ, and the ideal of countable dimensional subsets of ℝ. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of ℝ with any compactly countable dimensional subset of ℝ has first category.

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This is an author-produced, peer-reviewed version of this article. © 2009, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License ( The final, definitive version of this document can be found online at Topology and its Applications, doi: 10.1016/j.topol.2009.03.058

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