UID:
almahu_9949462255402882
Umfang:
1 online resource (219 p.)
ISBN:
9783110213225
,
9783110494969
Serie:
De Gruyter Expositions in Mathematics , 50
Inhalt:
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|G| minimal right ideals. In the third part, using the semigroup βG, 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 ω-resolvable, and consequently, can be partitioned into ω 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.
Anmerkung:
Frontmatter --
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Preface --
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Contents --
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1 Topological Groups --
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2 Ultrafilters --
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3 Topological Spaces with Extremal Properties --
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4 Left Invariant Topologies and Strongly Discrete Filters --
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5 Topological Groups with Extremal Properties --
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6 The Semigroup βS --
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7 Ultrafilter Semigroups --
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8 Finite Groups in βG --
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9 Ideal Structure of βG --
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10 Almost Maximal Topological Groups --
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11 Almost Maximal Spaces --
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12 Resolvability --
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13 Open Problems --
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Bibliography --
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Index
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Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Expositions in Mathematics Backlist eBook Package, De Gruyter, 9783110494969
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2010, De Gruyter, 9783110233544
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2010, De Gruyter, 9783110233551
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2010, De Gruyter, 9783110233636
Weitere Ausg.:
ISBN 9783110204223
Sprache:
Englisch
Fachgebiete:
Mathematik
DOI:
10.1515/9783110213225
URL:
https://doi.org/10.1515/9783110213225
URL:
https://www.degruyter.com/isbn/9783110213225
URL:
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