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II Workshop on Coverings, Selections and Games in Topology
December 19-22, 2005
University of Lecce
Lecce, Italy

Organizers
(Organizing Committee) Cosimo Guido, Anna Frascella, Domenico Lenzi, Gabriella Zammillo. (Scientific Committee) Liljana Babinkostova, Cosimo Guido, Ljubisa Kocinac, Marion Scheepers, Boaz Tsaban

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The combinatorics of the Baire group
by
Michal Machura
Institute of Mathematics, Bar Ilan University, Ramat Gan, Israel
Coauthors: Boaz Tsaban

We study subgroups of the Baire group ZN, 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 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.

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.

Paper reference: arXiv:math.GN/0508146

Date received: September 18, 2005

Copyright © 2005 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 # caqh-04.