The Continuum Hypothesis implies an Erdö-Sierpiński like duality between the ideal of first category subsets of ℝℕ, and the ideal of countable dimensional subsets of ℝℕ. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of ℝℕ with any compactly countable dimensional subset of ℝℕ has first category.
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 (https://creativecommons.org/licenses/by-nc-nd/4.0/). The final, definitive version of this document can be found online at Topology and its Applications, doi: 10.1016/j.topol.2009.03.058
Liljana Babinkostova and Marion Scheepers. "Weakly Infinite Dimensional Subsets of RN" Topology and its Applications
Available at: http://works.bepress.com/marion_scheepers/1/