Strong measure zero in separable metric spaces and Polish groups

被引：2

作者：

Hrusak, Michael ^{[1
]}

Wohofsky, Wolfgang ^{[2
]}

Zindulka, Ondrej ^{[3
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Ciudad Univ, Mexico City 04510, DF, Mexico

[2] Tech Univ Wien, Inst Diskrete Mathemat & Geometrie, Wiedner Hauptstr 8-10-104, A-1040 Vienna, Austria

[3] Czech Tech Univ, Fac Civil Engn, Dept Math, Thakurova 7, Prague 16000 6, Czech Republic

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2016年 / 55卷 / 1-2期

关键词：

Strong measure zero; Separable metric space; Small ball property; Polish group; Elastic group; Baer-Specker group Z(omega); Galvin-Mycielski-Solovay theorem; Meager; Uniformly meager; Translation; omega-Translatable; Uniformity number; Rothberger; SATURATED IDEALS; SETS; MAXIMUM;

D O I：

10.1007/s00153-015-0459-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 . 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 SteprAns (Ann Pure Appl Logic 140(1-3):52-59, 2006).

引用

页码：105 / 131

页数：27