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Squares of Menger-bounded groups

Michal Machura·Saharon Shelah·Boaz Tsaban
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Abstract

Using the Continuum Hyporthesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baer-Specker group Z^N, whose square is not Menger-bounded. This settles a major open problem concerning boundedness notions for groups, and implies that Menger-bounded groups need not be Scheepers-bounded. This also answers some questions of Banakh, Nickolas, and Sanchis.

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Michal Machura, Saharon Shelah, Boaz Tsaban. 2006-11-12. Squares of Menger-bounded groups. https://doi.org/10.1090/s0002-9947-09-05169-1

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