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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2009
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| Online Zugang: | 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 |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
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| ISSN: | 1726-3255 |