English

The descriptive look at the size of subsets of groups

General Topology 2017-03-02 v1

Abstract

We explore the Borel complexity of some basic families of subsets of a countable group (large, small, thin, sparse and other) defined by the size of their elements. Applying the obtained results to the Stone-\v{C}ech compactification βG\beta G of GG, we prove, in particular, that the closure of the minimal ideal of βG\beta G is of type FσδF_{\sigma\delta}.

Keywords

Cite

@article{arxiv.1703.00174,
  title  = {The descriptive look at the size of subsets of groups},
  author = {Igor Protasov and Taras Banakh and Ksenia Protasova},
  journal= {arXiv preprint arXiv:1703.00174},
  year   = {2017}
}