Weakly infinite dimensional subsets of R^N

Details Weakly infinite dimensional subsets of R^N Weakly infinite dimensional subsets of R^N

2008-11-22

arxiv.org/abs/0811.3661v2

Mathematics

General Topology

16 pages, corrected Statements of Theorem 6 and Lemma 8, Inserted Problem 1, Inserted remarks by R. Pol, solving Problem 3, in

Scientific paper

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.

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