TY - JOUR
T1 - Squares of menger-bounded groups
AU - Machura, Michal
AU - Shelah, Saharon
AU - Tsaban, Boaz
PY - 2010/4
Y1 - 2010/4
N2 - 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 ℤℕ, 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.
AB - 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 ℤℕ, 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.
UR - http://www.scopus.com/inward/record.url?scp=77950883262&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-09-05169-1
DO - 10.1090/S0002-9947-09-05169-1
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:77950883262
SN - 0002-9947
VL - 362
SP - 1751
EP - 1764
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 4
ER -