Strong measure zero in separable metric spaces and Polish groups

Archive for Mathematical Logic 55 (1-2):105-131 (2016)
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Abstract

The notion of strong measure zero is studied in the context of Polish groups and general separable metric spaces. An extension of a theorem of Galvin, Mycielski and Solovay is given, whereas the theorem is shown to fail for the Baer–Specker group Zω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{Z}^{\omega}}}$$\end{document}. The uniformity number of the ideal of strong measure zero subsets of a separable metric space is examined, providing solutions to several problems of Miller and Steprāns :52–59, 2006).

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Meager-Additive Sets in Topological Groups.Ondřej Zindulka - 2022 - Journal of Symbolic Logic 87 (3):1046-1064.

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