ar X iv : m at h / 05 08 14 6 v 4 [ m at h . G N ] 1 6 N ov 2 00 6 THE COMBINATORICS OF THE BAIRE GROUP
نویسنده
چکیده
We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Kočinac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Kočinac, and Scheepers.
منابع مشابه
ar X iv : m at h / 05 08 14 6 v 2 [ m at h . G N ] 1 8 A ug 2 00 5 THE COMBINATORICS OF THE BAIRE GROUP
We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Kočinac, and Scheepers. We also show that, while the Menger Conjectu...
متن کاملar X iv : m at h / 05 08 14 6 v 1 [ m at h . G N ] 8 A ug 2 00 5 THE COMBINATORICS OF THE BAIRE GROUP
We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Kočinac, and Scheepers. We also show that, while the Menger Conjectu...
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.
متن کاملar X iv : m at h / 05 08 14 6 v 3 [ m at h . G N ] 2 9 Se p 20 05 THE COMBINATORICS OF THE BAIRE GROUP
We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Kočinac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babink...
متن کاملar 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.
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