Squares of Menger-bounded groups
一般拓扑
2010-11-05 v4 逻辑
摘要
Using the Continuum Hyporthesis, we prove that there is a Menger-bounded (also called o-bounded) subgroup of the Baer-Specker group Z^N, whose square is not Menger-bounded. This settles a major open problem concerning boundedness notions for groups, and implies that Menger-bounded groups need not be Scheepers-bounded. This also answers some questions of Banakh, Nickolas, and Sanchis.
引用
@article{arxiv.math/0611353,
title = {Squares of Menger-bounded groups},
author = {Michal Machura and Saharon Shelah and Boaz Tsaban},
journal= {arXiv preprint arXiv:math/0611353},
year = {2010}
}