M ay 2 00 7 SQUARES OF MENGER - BOUNDED GROUPS
نویسنده
چکیده
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 Mengerbounded. 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.
منابع مشابه
ar X iv : m at h / 06 11 35 3 v 1 [ m at h . G N ] 1 2 N ov 2 00 6 SQUARES OF MENGER - BOUNDED GROUPS
Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baire 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.
متن کاملar X iv : m at h / 06 11 35 3 v 2 [ m at h . G N ] 1 6 N ov 2 00 6 SQUARES OF MENGER - BOUNDED GROUPS
Using a portion of the Continuum Hypothesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baire 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.
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