Descriptive complexity of the sizes of subsets of groups

  • T. O. Banakh
  • I. V. Protasov Kyiv Nat. Taras Shevchenko Univ.
  • K. D. Protasova


We study the Borel complexity of some basic families of subsets of a countable group (large, small, thin, rarefied, etc.) determined by the sizes of their elements. The obtained results are applied to the Czech – Stone compactification $\beta G$ of the group $G$. In particular, it is shown that the closure of the minimal ideal $\beta G$ has the $F_{\sigma \delta}$ type.
How to Cite
Banakh, T. O., I. V. Protasov, and K. D. Protasova. “Descriptive Complexity of the Sizes of Subsets of groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 9, Sept. 2017, pp. 1280-3,
Short communications