  The Continuum Hypothesis implies an Erd\"os-Sierpi\'nski 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.
