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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 9, pp. 1280–1283, September, 2017.
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Banakh, T.O., Protasov, I.V. & Protasova, K.D. Descriptive Complexity of the Sizes of Subsets of Groups. Ukr Math J 69, 1485–1489 (2018). https://doi.org/10.1007/s11253-018-1448-5
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DOI: https://doi.org/10.1007/s11253-018-1448-5