Squares of Menger-bounded groups

Details Squares of Menger-bounded groups Squares of Menger-bounded groups

2006-11-12

arxiv.org/abs/math/0611353v4

Transactions of the American Mathematical Society 362 (2010), 1751-1764

Mathematics

General Topology

Scientific paper

10.1090/S0002-9947-09-05169-1

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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