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2004-2005 Products of special sets of real numbers.
Boaz Tsaban, Tomasz Weiss
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Real Anal. Exchange 30(2): 819-836 (2004-2005).


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: $\mathsf{S}_fin(\Omega,\Omega^{gp})\cap\mathsf{S}_1(\mathcal{O},\mathcal{O})=\mathsf{S}_1(\Omega,\Omega^{gp})$, and Borel's Conjecture for $\mathsf{S}_1(\Omega,\Omega)$ (or just $\mathsf{S}_1(\Omega,\Omega^{gp})$) implies Borel's Conjecture.

These results extend results of Scheepers and Miller, respectively.


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Boaz Tsaban. Tomasz Weiss. "Products of special sets of real numbers.." Real Anal. Exchange 30 (2) 819 - 836, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

zbMATH: 1103.03043
MathSciNet: MR2177439

Primary: 26A03
Secondary: 03E75 , 37F20

Keywords: products. , Special sets of real numbers

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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