Geodesic
Ultracompanions of subsets of a group
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 257-265

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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.
Classification : 20F69, 22A15, 54D35
Keywords: Stone-Čech compactification; ultracompanion; sparse and discrete subsets of a group 
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     title = {Ultracompanions of subsets of a group},
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Protasov, I.; Slobodianiuk, S. Ultracompanions of subsets of a group. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 2, pp. 257-265. http://geodesic.mathdoc.fr/item/CMUC_2014__55_2_a10/