Algebra in the Stone-Čech compactification: applications to topologies on groups
For every discrete group G, the Stone-Čech compactification βG of G has a natural structure of compact right topological semigroup. Assume that G is endowed with some left invariant topology I and let τ¯ be the set of all ultrafilters on G converging to the unit of G in I. Then τ¯ is a closed subsem...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/153384 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Algebra in the Stone-Čech compactification: applications to topologies on groups / I.V. Protasov // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 1. — С. 83–110. — Бібліогр.: 62 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734523874148352 |
|---|---|
| author | Protasov, I.V. |
| author_facet | Protasov, I.V. |
| citation_txt | Algebra in the Stone-Čech compactification: applications to topologies on groups / I.V. Protasov // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 1. — С. 83–110. — Бібліогр.: 62 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | For every discrete group G, the Stone-Čech compactification βG of G has a natural structure of compact right topological semigroup. Assume that G is endowed with some left invariant topology I and let τ¯ be the set of all ultrafilters on G converging to the unit of G in I. Then τ¯ is a closed subsemigroup of βG. We survey the results clarifying the interplays between the algebraic properties of τ¯ and the topological properties of (G,I)
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 βG and G∗, Ramsey-like ultrafilters, Maximality, Refinements, Resolvability, Potential compactness and ultraranks, Selected open questions.
|
| first_indexed | 2025-12-07T19:43:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153384 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:43:22Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Protasov, I.V. 2019-06-14T03:48:18Z 2019-06-14T03:48:18Z 2009 Algebra in the Stone-Čech compactification: applications to topologies on groups / I.V. Protasov // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 1. — С. 83–110. — Бібліогр.: 62 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 22A05, 22A15, 22A20, 05A18, 54A35, 54D80. https://nasplib.isofts.kiev.ua/handle/123456789/153384 For every discrete group G, the Stone-Čech compactification βG of G has a natural structure of compact right topological semigroup. Assume that G is endowed with some left invariant topology I and let τ¯ be the set of all ultrafilters on G converging to the unit of G in I. Then τ¯ is a closed subsemigroup of βG. We survey the results clarifying the interplays between the algebraic properties of τ¯ and the topological properties of (G,I)
 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 βG and G∗, Ramsey-like ultrafilters, Maximality, Refinements, Resolvability, Potential compactness and ultraranks, Selected open questions. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Algebra in the Stone-Čech compactification: applications to topologies on groups Article published earlier |
| spellingShingle | Algebra in the Stone-Čech compactification: applications to topologies on groups Protasov, I.V. |
| title | Algebra in the Stone-Čech compactification: applications to topologies on groups |
| title_full | Algebra in the Stone-Čech compactification: applications to topologies on groups |
| title_fullStr | Algebra in the Stone-Čech compactification: applications to topologies on groups |
| title_full_unstemmed | Algebra in the Stone-Čech compactification: applications to topologies on groups |
| title_short | Algebra in the Stone-Čech compactification: applications to topologies on groups |
| title_sort | algebra in the stone-čech compactification: applications to topologies on groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153384 |
| work_keys_str_mv | AT protasoviv algebrainthestonecechcompactificationapplicationstotopologiesongroups |