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

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**Yevhen G. Zelenyuk**, University of the Witwatersrand, Johannesburg, South Africa.

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De Gruyter 2011-03-17, Berlin
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**Book Description **Walter De Gmbh Gruyter Mrz 2011, 2011. Buch. Book Condition: Neu. Neuware - 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 aboutultrafilters. 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 219 pp. Englisch. Bookseller Inventory # 9783110204223

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Published by
Walter De Gmbh Gruyter Mrz 2011
(2011)

ISBN 10: 3110204223
ISBN 13: 9783110204223

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**Book Description **Walter De Gmbh Gruyter Mrz 2011, 2011. Buch. Book Condition: Neu. Neuware - 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 aboutultrafilters. 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 219 pp. Englisch. Bookseller Inventory # 9783110204223

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Published by
Walter De Gmbh Gruyter Mrz 2011
(2011)

ISBN 10: 3110204223
ISBN 13: 9783110204223

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**Book Description **Walter De Gmbh Gruyter Mrz 2011, 2011. Buch. Book Condition: Neu. Neuware - 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 aboutultrafilters. 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 219 pp. Englisch. Bookseller Inventory # 9783110204223

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Published by
Walter De Gmbh Gruyter Mrz 2011
(2011)

ISBN 10: 3110204223
ISBN 13: 9783110204223

New
Quantity Available: 1

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**Book Description **Walter De Gmbh Gruyter Mrz 2011, 2011. Buch. Book Condition: Neu. Neuware - 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 betaG 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 betaG contains no nontrivial finite groups. Also the ideal structure of betaG is investigated. In particular, one shows that for every infinite Abelian group G , betaG contains 2 2 G minimal right ideals. In the third part, using the semigroup betaG , almost maximal topological and left topological groups are constructed and their ultrafilter semigroups are examined. Projectives in the category of finite semigroups are characterized. Also one shows that every infinite Abelian group with finitely many elements of order 2 is absolutely -resolvable, and consequently, can be partitioned into subsets such that every coset modulo infinite subgroup meets each subset of the partition. The book concludes with a list of open problems in the field. Some familiarity with set theory, algebra and topology is presupposed. But in general, the book is almost self-contained. It is aimed at graduate students and researchers working in topological algebra and adjacent areas. 219 pp. Englisch. Bookseller Inventory # 9783110204223

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Published by
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(2011)

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ISBN 13: 9783110204223

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**Book Description **De Gruyter, 2011. Hardcover. Book Condition: New. book. Bookseller Inventory # M3110204223

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Published by
De Gruyter, Germany
(2011)

ISBN 10: 3110204223
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**Book Description **De Gruyter, Germany, 2011. Hardback. Book Condition: New. Language: English . Brand New Book. 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 aboutultrafilters. 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. Bookseller Inventory # LIB9783110204223

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