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arXiv · 1703.00174

The descriptive look at the size of subsets of groups

Igor Protasov·Taras Banakh·Ksenia Protasova
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Abstract

We explore the Borel complexity of some basic families of subsets of a countable group (large, small, thin, sparse and other) defined by the size of their elements. Applying the obtained results to the Stone-\v{C}ech compactification $\beta G$ of $G$, we prove, in particular, that the closure of the minimal ideal of $\beta G$ is of type $F_{\sigma\delta}$.

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Igor Protasov, Taras Banakh, Ksenia Protasova. 2017-03-01. The descriptive look at the size of subsets of groups. https://arxiv.org/abs/1703.00174

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