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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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-153384 |
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dspace |
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irk-123456789-1533842019-06-15T01:26:33Z Algebra in the Stone-Čech compactification: applications to topologies on groups Protasov, I.V. 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. 2009 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/153384 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Protasov, I.V. |
| spellingShingle |
Protasov, I.V. Algebra in the Stone-Čech compactification: applications to topologies on groups Algebra and Discrete Mathematics |
| author_facet |
Protasov, I.V. |
| author_sort |
Protasov, I.V. |
| title |
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_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_sort |
algebra in the stone-čech compactification: applications to topologies on groups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153384 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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AT protasoviv algebrainthestonecechcompactificationapplicationstotopologiesongroups |
| first_indexed |
2023-05-20T17:38:49Z |
| last_indexed |
2023-05-20T17:38:49Z |
| _version_ |
1796153770620485632 |