English

Additivity of the Gerlits--Nagy property and concentrated sets

General Topology 2012-06-01 v1 Combinatorics Logic

Abstract

We settle all problems posed by Scheepers, in his tribute paper to Gerlits, concerning the additivity of the Gerlits--Nagy property and related additivity numbers. We apply these results to compute the minimal number of concentrated sets of reals (in the sense of Besicovitch) whose union, when multiplied with a Gerlits--Nagy space, need not have Rothberger's property. We apply these methods to construct a large family of spaces, whose product with every Hurewicz space has Menger's property.

Keywords

Cite

@article{arxiv.1205.6824,
  title  = {Additivity of the Gerlits--Nagy property and concentrated sets},
  author = {Boaz Tsaban and Lyubomyr Zdomskyy},
  journal= {arXiv preprint arXiv:1205.6824},
  year   = {2012}
}