Scattered Subsets of Groups

• Date: 2015
• Main Authors: Banakh, T. O., Protasov, I. V., Slobodianiuk, S. V., Банах, Т. О., Протасов, І. В., Слободянюк, С. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1983
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...