Straightening Theorem for bounded Abelian groups

被引：1

作者：

de Leo, Lorenzo ^{[1
]}

Dikranjan, Dikran ^{[1
]}

机构：

[1] Univ Udine, Dept Math & Informat, I-33100 Udine, Italy

来源：

TOPOLOGY AND ITS APPLICATIONS | 2008年 / 155卷 / 17-18期

关键词：

Bohr topology; Bounded Abelian group; Ulm-Kaplansky invariants;

D O I：

10.1016/j.topol.2007.07.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that every continuous function f with f (0) = 0 between two bounded Abelian groups G and H equipped with the Bohr topology coincides with a homomorphism when restricted to an infinite subset of the domain. This extends the main results of [K. Kunen, Bohr topology and partition theorems for vector spaces, Topology Appl. 90 (1998) 97-107, D. Dikranjan, S. Watson, A solution to van Douwen's problem on the Bohr topologies. J. Pure Appl. Algebra 163 (2001) 147-158]. Moreover, we give several applications and we answer a question of [B. Givens. K. Kunen, Chromatic numbers and Bohr topologies. Topology Appl. 131 (2) (2003) 189-202]. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：2158 / 2176

页数：19

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