2017
Том 69
№ 9

All Issues

Descriptive complexity of the sizes of subsets of groups

Banakh T. O., Protasov I. V., Protasova K. D.


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.