Squares of menger-bounded groups

Michal Machura, Saharon Shelah, Boaz Tsaban

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baer-Specker group ℤ, 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.

Original languageEnglish
Pages (from-to)1751-1764
Number of pages14
JournalTransactions of the American Mathematical Society
Issue number4
StatePublished - Apr 2010


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