o-bounded groups and other topological groups with strong combinatorial properties
General Topology
2010-11-02 v7 Combinatorics
Group Theory
Logic
Abstract
We construct several topological groups with very strong combinatorial properties. In particular, we give simple examples of subgroups of the real line R (thus strictly o-bounded) which have the Hurewicz property but are not sigma-compact, and show that the product of two o-bounded subgroups of R^N may fail to be o-bounded, even when they satisfy the stronger property S1(Borel_Omega,Borel_Omega). This solves a problem of Tkacenko and Hernandez, and extends independent solutions of Krawczyk and Michalewski and of Banakh, Nickolas, and Sanchis. We also construct separable metrizable groups G of size continuum such that every countable Borel omega-cover of G contains a gamma-cover of G.
Cite
@article{arxiv.math/0307225,
title = {o-bounded groups and other topological groups with strong combinatorial properties},
author = {Boaz Tsaban},
journal= {arXiv preprint arXiv:math/0307225},
year = {2010}
}
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