SPM Bulletin 11

This issue contains, in addition to the usual contents, a special festive announcement: A book. This book by Banakh and Zdomsky seems to be the first in a planned series by these authors. We believe that the book will become a cornerstone in many future mathematical investigations, in particular in the field of infinite-combinatorial topology. The book's preliminary version is available online, as seen in the announcement, and the readers of the SPM Bulletin are encouraged to take a look and make comments. Zdomsky has also made two detailed contributions to this issue. This is the ideal form of a contribution to the SPM Bulletin, and we urge all contributors to consider this possibility from time to time. 1 Editor's note; 2 Research announcements; 2.1 On subclasses of weak Asplund spaces; 2.2 The number of translates of a closed nowhere dense set required to cover a Polish group; 2.3 More on convexity numbers of closed sets in R^n; 2.4 A new book: Coherence of Semifilters; 3 Characterization of topological spaces with (strictly) o-bounded free topological group; 4 An equivalent of SPM Bulletin 2's Problem of the month; 5 Boise Extravaganza In Set Theory (March 25--27, 2005); 6 Problem of the Issue; 7 Problems from earlier issues; ReferencesComment: Change of notatio

Strong measure zero in Polish groups

The notion of strong measure zero is studied in the context of Polish groups. In particular, the extent to which the theorem of Galvin, Mycielski and Solovay holds in the context of an arbitrary Polish group is studied. Hausdorff measure and dimension is used to characterize strong measure zero. The products of strong measure zero sets are examined. Sharp measure zero, a notion stronger that strong measure zero, is shown to be related to meageradditive sets in the Cantor set and Polish groups by a theorem very similar to the theorem of Galvin, Mycielski and Solovay