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Products of special sets of real numbers

Logic 2010-08-02 v4 Combinatorics General Topology

Abstract

We describe a simple machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are: 1. The product of a meager/null-additive set and a strong measure zero/strongly meager set in the Cantor space has strong measure zero/is strongly meager, respectively. 2. Using Scheepers' notation for selection principles: Sfin(Omega,Omega^gp)\cap S1(O,O)=S1(Omega,Omega^gp), and Borel's Conjecture for S1(Omega,Omega) (or just S1(Omega,Omega^gp)) implies Borel's Conjecture. These results extend results of Scheepers and Miller, respectively.

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Cite

@article{arxiv.math/0307226,
  title  = {Products of special sets of real numbers},
  author = {Boaz Tsaban and Tomasz Weiss},
  journal= {arXiv preprint arXiv:math/0307226},
  year   = {2010}
}

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