Mathematics – General Topology
Scientific paper
2003-07-16
Proceedings of the American Mathematical Society 134 (2006), 881--891
Mathematics
General Topology
Small updates
Scientific paper
10.1090/S0002-9939-05-08034-2
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.
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