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Ukrainian Mathematical Journal

, Volume 69, Issue 9, pp 1485–1489 | Cite as

Descriptive Complexity of the Sizes of Subsets of Groups

  • T. O. Banakh
  • I. V. Protasov
  • K. D. Protasova
Article
  • 29 Downloads

We study the Borel complexity of some basic families of subsets of a countable group (large, small, thin, sparse, etc.) determined by the sizes of their elements. The obtained results are applied to the Čech–Stone compactification 𝛽G of the group G. In particular, it is shown that the closure of the minimal ideal 𝛽G has the F𝜎𝛿 type.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • T. O. Banakh
    • 1
  • I. V. Protasov
    • 2
  • K. D. Protasova
    • 2
  1. 1.Franko Lviv National UniversityLvivUkraine
  2. 2.Shevchenko Kyiv National UniversityKyivUkraine

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