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Ultrafilters and topologies on groups /
This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results about ultrafilters. Topics covered include: topological...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; New York :
De Gruyter,
©2011.
|
| Colección: | De Gruyter expositions in mathematics ;
50. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Zelenyuk, Yevhen G. | |
| 245 | 1 | 0 | |a Ultrafilters and topologies on groups / |c Yevhen G. Zelenyuk. |
| 260 | |a Berlin ; |a New York : |b De Gruyter, |c ©2011. | ||
| 300 | |a 1 online resource (viii, 219 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a De Gruyter expositions in mathematics, |x 0938-6572 ; |v 50 | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results about ultrafilters. Topics covered include: topological and left topological groups, ultrafilter semigroups, local homomorphisms and automorphisms, subgroups and ideal structure of ßG, almost maximal spaces and projectives of finite semigroups, resolvability of groups. This is a self-contained book aimed at graduate students and researchers working in topological algebra and adjacent areas. From the contents: Topological Groups Ultrafilters Topological Spaces with Extremal Properties Left Invariant Topologies and Strongly Discrete Filters Topological Groups with Extremal Properties The Semigroup ßS Ultrafilter Semigroups Finite Groups in ßG Ideal Structure of ßS Almost Maximal Topological Groups and Spaces Resolvability Open Problems. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a In English. | ||
| 505 | 0 | 0 | |6 880-01 |t Frontmatter -- |t Preface -- |t Contents -- |t 1 Topological Groups -- |t 2 Ultrafilters -- |t 3 Topological Spaces with Extremal Properties -- |t 4 Left Invariant Topologies and Strongly Discrete Filters -- |t 5 Topological Groups with Extremal Properties -- |t 6 The Semigroup [beta]S -- |t 7 Ultrafilter Semigroups -- |t 8 Finite Groups in [beta]G -- |t 9 Ideal Structure of [beta]G -- |t 10 Almost Maximal Topological Groups -- |t 11 Almost Maximal Spaces -- |t 12 Resolvability -- |t 13 Open Problems -- |t Bibliography -- |t Index. |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Topological group theory. | |
| 650 | 0 | |a Ultrafilters (Mathematics) | |
| 650 | 4 | |a Filter. | |
| 650 | 4 | |a Gruppentheorie. | |
| 650 | 4 | |a Topologie. | |
| 650 | 6 | |a Ultrafiltres (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Ultrafilters (Mathematics) |2 fast | |
| 650 | 7 | |a Topologische Gruppe |2 gnd | |
| 650 | 7 | |a Ultrafilter |g Mathematik |2 gnd | |
| 776 | 0 | 8 | |i Print version: |a Zelenyuk, Yevhen G. |t Ultrafilters and topologies on groups. |d Berlin ; New York : De Gruyter, ©2011 |w (DLC) 2010050782 |
| 830 | 0 | |a De Gruyter expositions in mathematics ; |v 50. |x 0938-6572 | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=388077 |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |t Frontmatter -- |t Preface -- |t Contents -- |t 1 Topological Groups -- |t 2 Ultrafilters -- |t 3 Topological Spaces with Extremal Properties -- |t 4 Left Invariant Topologies and Strongly Discrete Filters -- |t 5 Topological Groups with Extremal Properties -- |t 6 The Semigroup βS -- |t 7 Ultrafilter Semigroups -- |t 8 Finite Groups in βG -- |t 9 Ideal Structure of βG -- |t 10 Almost Maximal Topological Groups -- |t 11 Almost Maximal Spaces -- |t 12 Resolvability -- |t 13 Open Problems -- |t Bibliography -- |t Index. |
| 880 | |6 520-00/(S |a This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results about ultrafilters. The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5, introduces to topological groups and ultrafilters insofar as the semigroup operation on ultrafilters is not required. Constructions of some important topological groups are given. In particular, that of an extremally disconnected topological group based on a Ramsey ultrafilter. Also one shows that every infinite group admits a nondiscrete zero-dimensional topology in which all translations and the inversion are continuous. In the second part, Chapters 6 through 9, the Stone-Cêch compactification βG of a discrete group G is studied. For this, a special technique based on the concepts of a local left group and a local homomorphism is developed. One proves that if G is a countable torsion free group, then βG contains no nontrivial finite groups. Also the ideal structure of βG is investigated. In particular, one shows that for every infinite Abelian group G, βG contains 22 | ||
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