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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York :
De Gruyter,
©2011.
|
| Schriftenreihe: | De Gruyter expositions in mathematics ;
50. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (viii, 219 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110213225 3110213222 1283164728 9781283164726 3110204223 9783110204223 9786613164728 6613164720 |
| ISSN: | 0938-6572 ; |
Internformat
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| 245 | 1 | 0 | |a Ultrafilters and topologies on groups / |c Yevhen G. Zelenyuk. |
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| 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. |
| 650 | 0 | |a Topological group theory. | |
| 650 | 0 | |a Ultrafilters (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85139468 | |
| 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 |0 http://d-nb.info/gnd/4135793-0 | |
| 650 | 7 | |a Ultrafilter |g Mathematik |2 gnd |0 http://d-nb.info/gnd/4273543-9 | |
| 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 |0 http://id.loc.gov/authorities/names/n90653843 | |
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| 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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Datensatz im Suchindex
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| _version_ | 1816881770888429568 |
| adam_text | |
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| author | Zelenyuk, Yevhen G. |
| author_facet | Zelenyuk, Yevhen G. |
| author_role | |
| author_sort | Zelenyuk, Yevhen G. |
| author_variant | y g z yg ygz |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166.195 .Z45 2011eb |
| callnumber-search | QA166.195 .Z45 2011eb |
| callnumber-sort | QA 3166.195 Z45 42011EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Frontmatter -- Preface -- Contents -- 1 Topological Groups -- 2 Ultrafilters -- 3 Topological Spaces with Extremal Properties -- 4 Left Invariant Topologies and Strongly Discrete Filters -- 5 Topological Groups with Extremal Properties -- 6 The Semigroup [beta]S -- 7 Ultrafilter Semigroups -- 8 Finite Groups in [beta]G -- 9 Ideal Structure of [beta]G -- 10 Almost Maximal Topological Groups -- 11 Almost Maximal Spaces -- 12 Resolvability -- 13 Open Problems -- Bibliography -- Index. |
| ctrlnum | (OCoLC)754713543 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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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.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="6">880-01</subfield><subfield code="t">Frontmatter --</subfield><subfield code="t">Preface --</subfield><subfield code="t">Contents --</subfield><subfield code="t">1 Topological Groups --</subfield><subfield code="t">2 Ultrafilters --</subfield><subfield code="t">3 Topological Spaces with Extremal Properties --</subfield><subfield code="t">4 Left Invariant Topologies and Strongly Discrete Filters --</subfield><subfield code="t">5 Topological Groups with Extremal Properties --</subfield><subfield code="t">6 The Semigroup [beta]S --</subfield><subfield code="t">7 Ultrafilter Semigroups --</subfield><subfield code="t">8 Finite Groups in [beta]G --</subfield><subfield code="t">9 Ideal Structure of [beta]G --</subfield><subfield code="t">10 Almost Maximal Topological Groups --</subfield><subfield code="t">11 Almost Maximal Spaces --</subfield><subfield code="t">12 Resolvability --</subfield><subfield code="t">13 Open Problems --</subfield><subfield code="t">Bibliography --</subfield><subfield code="t">Index.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Topological group theory.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Ultrafilters (Mathematics)</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85139468</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Filter.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gruppentheorie.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topologie.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Ultrafiltres (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Algebra</subfield><subfield code="x">Linear.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Ultrafilters (Mathematics)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Topologische Gruppe</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4135793-0</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Ultrafilter</subfield><subfield code="g">Mathematik</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4273543-9</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Zelenyuk, Yevhen G.</subfield><subfield code="t">Ultrafilters and topologies on groups.</subfield><subfield code="d">Berlin ; New York : De Gruyter, ©2011</subfield><subfield code="w">(DLC) 2010050782</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter expositions in mathematics ;</subfield><subfield code="v">50.</subfield><subfield code="x">0938-6572</subfield><subfield code="0">http://id.loc.gov/authorities/names/n90653843</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=388077</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="0" ind2="0"><subfield code="6">505-01/(S</subfield><subfield code="t">Frontmatter --</subfield><subfield code="t">Preface --</subfield><subfield code="t">Contents --</subfield><subfield code="t">1 Topological Groups --</subfield><subfield code="t">2 Ultrafilters --</subfield><subfield code="t">3 Topological Spaces with Extremal Properties --</subfield><subfield code="t">4 Left Invariant Topologies and Strongly Discrete Filters --</subfield><subfield code="t">5 Topological Groups with Extremal Properties --</subfield><subfield code="t">6 The Semigroup βS --</subfield><subfield code="t">7 Ultrafilter Semigroups --</subfield><subfield code="t">8 Finite Groups in βG --</subfield><subfield code="t">9 Ideal Structure of βG --</subfield><subfield code="t">10 Almost Maximal Topological Groups --</subfield><subfield code="t">11 Almost Maximal Spaces --</subfield><subfield code="t">12 Resolvability --</subfield><subfield code="t">13 Open Problems --</subfield><subfield code="t">Bibliography --</subfield><subfield code="t">Index.</subfield></datafield><datafield tag="880" ind1=" " ind2=" "><subfield code="6">520-00/(S</subfield><subfield code="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. 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| id | ZDB-4-EBA-ocn754713543 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:00Z |
| institution | BVB |
| isbn | 9783110213225 3110213222 1283164728 9781283164726 3110204223 9783110204223 9786613164728 6613164720 |
| issn | 0938-6572 ; |
| language | English |
| oclc_num | 754713543 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (viii, 219 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter expositions in mathematics ; |
| series2 | De Gruyter expositions in mathematics, |
| spelling | Zelenyuk, Yevhen G. Ultrafilters and topologies on groups / Yevhen G. Zelenyuk. Berlin ; New York : De Gruyter, ©2011. 1 online resource (viii, 219 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter expositions in mathematics, 0938-6572 ; 50 Includes bibliographical references and index. 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. Print version record. In English. 880-01 Frontmatter -- Preface -- Contents -- 1 Topological Groups -- 2 Ultrafilters -- 3 Topological Spaces with Extremal Properties -- 4 Left Invariant Topologies and Strongly Discrete Filters -- 5 Topological Groups with Extremal Properties -- 6 The Semigroup [beta]S -- 7 Ultrafilter Semigroups -- 8 Finite Groups in [beta]G -- 9 Ideal Structure of [beta]G -- 10 Almost Maximal Topological Groups -- 11 Almost Maximal Spaces -- 12 Resolvability -- 13 Open Problems -- Bibliography -- Index. Topological group theory. Ultrafilters (Mathematics) http://id.loc.gov/authorities/subjects/sh85139468 Filter. Gruppentheorie. Topologie. Ultrafiltres (Mathématiques) MATHEMATICS Algebra Linear. bisacsh Ultrafilters (Mathematics) fast Topologische Gruppe gnd http://d-nb.info/gnd/4135793-0 Ultrafilter Mathematik gnd http://d-nb.info/gnd/4273543-9 Print version: Zelenyuk, Yevhen G. Ultrafilters and topologies on groups. Berlin ; New York : De Gruyter, ©2011 (DLC) 2010050782 De Gruyter expositions in mathematics ; 50. 0938-6572 http://id.loc.gov/authorities/names/n90653843 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=388077 Volltext 505-01/(S Frontmatter -- Preface -- Contents -- 1 Topological Groups -- 2 Ultrafilters -- 3 Topological Spaces with Extremal Properties -- 4 Left Invariant Topologies and Strongly Discrete Filters -- 5 Topological Groups with Extremal Properties -- 6 The Semigroup βS -- 7 Ultrafilter Semigroups -- 8 Finite Groups in βG -- 9 Ideal Structure of βG -- 10 Almost Maximal Topological Groups -- 11 Almost Maximal Spaces -- 12 Resolvability -- 13 Open Problems -- Bibliography -- Index. 520-00/(S 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 |
| spellingShingle | Zelenyuk, Yevhen G. Ultrafilters and topologies on groups / De Gruyter expositions in mathematics ; Frontmatter -- Preface -- Contents -- 1 Topological Groups -- 2 Ultrafilters -- 3 Topological Spaces with Extremal Properties -- 4 Left Invariant Topologies and Strongly Discrete Filters -- 5 Topological Groups with Extremal Properties -- 6 The Semigroup [beta]S -- 7 Ultrafilter Semigroups -- 8 Finite Groups in [beta]G -- 9 Ideal Structure of [beta]G -- 10 Almost Maximal Topological Groups -- 11 Almost Maximal Spaces -- 12 Resolvability -- 13 Open Problems -- Bibliography -- Index. Topological group theory. Ultrafilters (Mathematics) http://id.loc.gov/authorities/subjects/sh85139468 Filter. Gruppentheorie. Topologie. Ultrafiltres (Mathématiques) MATHEMATICS Algebra Linear. bisacsh Ultrafilters (Mathematics) fast Topologische Gruppe gnd http://d-nb.info/gnd/4135793-0 Ultrafilter Mathematik gnd http://d-nb.info/gnd/4273543-9 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85139468 http://d-nb.info/gnd/4135793-0 http://d-nb.info/gnd/4273543-9 |
| title | Ultrafilters and topologies on groups / |
| title_alt | Frontmatter -- Preface -- Contents -- 1 Topological Groups -- 2 Ultrafilters -- 3 Topological Spaces with Extremal Properties -- 4 Left Invariant Topologies and Strongly Discrete Filters -- 5 Topological Groups with Extremal Properties -- 6 The Semigroup [beta]S -- 7 Ultrafilter Semigroups -- 8 Finite Groups in [beta]G -- 9 Ideal Structure of [beta]G -- 10 Almost Maximal Topological Groups -- 11 Almost Maximal Spaces -- 12 Resolvability -- 13 Open Problems -- Bibliography -- Index. |
| title_auth | Ultrafilters and topologies on groups / |
| title_exact_search | Ultrafilters and topologies on groups / |
| title_full | Ultrafilters and topologies on groups / Yevhen G. Zelenyuk. |
| title_fullStr | Ultrafilters and topologies on groups / Yevhen G. Zelenyuk. |
| title_full_unstemmed | Ultrafilters and topologies on groups / Yevhen G. Zelenyuk. |
| title_short | Ultrafilters and topologies on groups / |
| title_sort | ultrafilters and topologies on groups |
| topic | Topological group theory. Ultrafilters (Mathematics) http://id.loc.gov/authorities/subjects/sh85139468 Filter. Gruppentheorie. Topologie. Ultrafiltres (Mathématiques) MATHEMATICS Algebra Linear. bisacsh Ultrafilters (Mathematics) fast Topologische Gruppe gnd http://d-nb.info/gnd/4135793-0 Ultrafilter Mathematik gnd http://d-nb.info/gnd/4273543-9 |
| topic_facet | Topological group theory. Ultrafilters (Mathematics) Filter. Gruppentheorie. Topologie. Ultrafiltres (Mathématiques) MATHEMATICS Algebra Linear. Topologische Gruppe Ultrafilter Mathematik |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=388077 |
| work_keys_str_mv | AT zelenyukyevheng ultrafiltersandtopologiesongroups |