Scattered Subsets of Groups

• Published in: Український математичний журнал
• Date: 2015
• Main Authors: Banakh, T.O., Protasov, I.V., Slobodianiuk, S.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/165482
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Scattered Subsets of Groups / T.O. Banakh, I.V. Protasov, S.V. Slobodianiuk // Український математичний журнал. — 2015. — Т. 67, № 3. — С. 304–312. — Бібліогр.: 28 назв. — англ.

We define scattered subsets of a group as asymptotic counterparts of the scattered subspaces of a topological space and prove that a subset A of a group G is scattered if and only if A does not contain any piecewise shifted IP -subsets. For an amenable group G and a scattered subspace A of G, we sho...