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The combinatorics of the Baire group
by
Boaz Tsaban
The combinatorics of the Baire group
Coauthors: Michał Machura
We study subgroups of ZN which possess group theoretic properties of boundedness type, analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). (The studied properties were introduced independently by Kocinac and Okunev.)
We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Kocinac, and Scheepers.
An informal thesis emerging from our study is that the Baire group is a "universal" group with respect to boundedness properties of groups.
We also show that, while the Menger Conjecture, when formulated for metrizable groups, is false, the corresponding version of the Hurewicz Conjecture is true. This achieves a goal set by Okunev to find an inner characterization of subgroups of s-compact groups.
This paper is available online at http://arxiv.org/abs/math.GN/0508146
Paper reference: arXiv:math.GN/0508146
Date received: March 14, 2006
Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # casb-06.