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Article

Protasov, I. ; Slobodianiuk, S.
Ultracompanions of subsets of a group. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 55 (2014), issue 2, pp. 257-265
MSC: 20F69, 22A15, 54D35 | MR 3193930 | Zbl 06391542
Keywords:
Stone-Čech compactification; ultracompanion; sparse and discrete subsets of a group
Summary:
Let $G$ be a group, $\beta G$ be the Stone-Čech compactification of $G$ endowed with the structure of a right topological semigroup and $G^*=\beta G\setminus G$. Given any subset $A$ of $G$ and $p\in G^*$, we define the $p$-companion $\Delta _p(A)= A^*\cap Gp$ of $A$, and characterize the subsets with finite and discrete ultracompanions.
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