2019
Том 71
№ 11

# Descriptive complexity of the sizes of subsets of groups

Abstract

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.

Citation Example: Banakh T. O., Protasov I. V., Protasova K. D. Descriptive complexity of the sizes of subsets of groups // Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1280-1283.

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