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
BanakhT. O., ProtasovI. V., and ProtasovaK. D. “Descriptive Complexity of the Sizes of Subsets of groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 9, Sept. 2017, pp. 1280-3,
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