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arXiv · 1308.1499

Ultracompanions of subsets of a group

I. Protasov·S. Slobodianiuk
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Abstract

Let $G$ be a group, $βG$ is the Stone-$\check{C}$ech compactification of $βG$ endowed with the structure of a right topological semigroup, $G^*=βG\setminus G$. Given any subset $A$ of $G$ and $p\in G^*$, we define the $p$-companion $\vt_p(A)=A^*\cap Gp$ of $A$, and characterize the subsets with finite and discrete ultracompanions.

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I. Protasov, S. Slobodianiuk. 2013-08-07. Ultracompanions of subsets of a group. https://arxiv.org/abs/1308.1499

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