Weakly infinite dimensional subsets of R^N
arXiv:0811.3661
Abstract
The Continuum Hypothesis implies an Erdös-Sierpiński like duality between the ideal of first category subsets of $\reals^{\naturals}$, and the ideal of countable dimensional subsets of $\reals^{\naturals}$. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of $\reals^{\naturals}$ with any compactly countable dimensional subset of $\reals^{\naturals}$ has first category.
16 pages, corrected Statements of Theorem 6 and Lemma 8, Inserted Problem 1, Inserted remarks by R. Pol, solving Problem 3, in "Added in Proof" section