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Algebra and Discrete Mathematics, 2009, выпуск 1, страницы 83–110
(Mi adm110)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
RESEARCH ARTICLE
Algebra in the Stone-$\check C$ech compactification: applications to topologies on groups
I. V. Protasov Department of Cybernetics, Kyiv National University, Volodimirska 64, Kyiv 01033, Ukraine
Аннотация:
For every discrete group $G$, the Stone-$\check{C}$ech compactification $\beta G$ of $G$ has a natural structure of compact right topological semigroup. Assume that $G$ is endowed with some left invariant topology $\Im$ and let $\overline{\tau}$ be the set of all ultrafilters on $G$ converging to the unit of $G$ in $\Im$. Then $\overline{\tau}$ is a closed subsemigroup of $\beta G$. We survey the results clarifying the interplays between the algebraic properties of $\overline{\tau}$ and the topological properties of $(G,\Im)$ and apply these results to solve some open problems in the topological group theory.
The paper consists of 13 sections: Filters on groups, Semigroup of ultrafilters, Ideals, Idempotents, Equations, Continuity in $\beta G$ and $G^*$, Ramsey-like ultrafilters, Maximality, Refinements, Resolvability, Potential compactness and ultraranks, Selected open questions.
Ключевые слова:
Stone-$\check{C}$ech compactification, product of ultrafilters, idempotents, ideals, maximality, resolvability, extremal disconnectedness.
Поступила в редакцию: 09.04.2009 Исправленный вариант: 02.05.2009
Образец цитирования:
I. V. Protasov, “Algebra in the Stone-$\check C$ech compactification: applications to topologies on groups”, Algebra Discrete Math., 2009, no. 1, 83–110
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm110 https://www.mathnet.ru/rus/adm/y2009/i1/p83
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