Ultracompanions of subsets of a group

I. Protasov; S. Slobodianiuk

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 2, page 257-265
  • ISSN: 0010-2628

Abstract

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Let G be a group, β G be the Stone-Čech compactification of G endowed with the structure of a right topological semigroup and G * = β G ∖ G . Given any subset A of G and p ∈ G * , we define the p -companion Δ p ( A ) = A * ∩ G p of A , and characterize the subsets with finite and discrete ultracompanions.

How to cite

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Protasov, I., and Slobodianiuk, S.. "Ultracompanions of subsets of a group." Commentationes Mathematicae Universitatis Carolinae 55.2 (2014): 257-265. <http://eudml.org/doc/261872>.

@article{Protasov2014,
abstract = {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.},
author = {Protasov, I., Slobodianiuk, S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Stone-Čech compactification; ultracompanion; sparse and discrete subsets of a group; Stone-Čech compactification; ultracompanion; sparse and discrete subsets of a group},
language = {eng},
number = {2},
pages = {257-265},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Ultracompanions of subsets of a group},
url = {http://eudml.org/doc/261872},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Protasov, I.
AU - Slobodianiuk, S.
TI - Ultracompanions of subsets of a group
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 2
SP - 257
EP - 265
AB - 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.
LA - eng
KW - Stone-Čech compactification; ultracompanion; sparse and discrete subsets of a group; Stone-Čech compactification; ultracompanion; sparse and discrete subsets of a group
UR - http://eudml.org/doc/261872
ER -

References

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