2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216781The 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" sectionGeneral Topology03E17, 03E50, 54D20, 54F45text