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Author : Sidney A. Morris
Publisher : MDPI
Page : 229 pages
File Size : 51,5 Mb
Release : 2018-09-27
Category : Electronic books
ISBN : 9783038422686
This book is a printed edition of the Special Issue "Topological Groups: Yesterday, Today, Tomorrow" that was published in Axioms
Author : Sidney A. Morris
Publisher : MDPI
Page : 160 pages
File Size : 44,6 Mb
Release : 2019-03-05
Category : Mathematics
ISBN : 9783038976448
Following the tremendous reception of our first volume on topological groups called "Topological Groups: Yesterday, Today, and Tomorrow", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.
Author : Taqdir Husain
Publisher : Courier Dover Publications
Page : 241 pages
File Size : 54,7 Mb
Release : 2018-02-15
Category : Mathematics
ISBN : 9780486819198
Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
Author : Sidney Morris
Publisher : Unknown
Page : 128 pages
File Size : 55,9 Mb
Release : 2019
Category : Electronic
ISBN : 3038976458
Following the tremendous reception of our first volume on topological groups called "Topological Groups: Yesterday, Today, and Tomorrow", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.
Author : Lev Semenovich Pontri︠a︡gin
Publisher : Unknown
Page : 322 pages
File Size : 40,7 Mb
Release : 1939
Category : Mathematics
ISBN : STANFORD:36105030753037
Author : Wolfgang Herfort,Karl H. Hofmann,Francesco G. Russo
Publisher : Walter de Gruyter GmbH & Co KG
Page : 354 pages
File Size : 53,6 Mb
Release : 2018-11-19
Category : Mathematics
ISBN : 9783110599190
This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples. Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin’s pioneering work generalizing to locally compact groups Iwasawa’s early investigations of the lattice of subgroups of abstract groups. Contents Part I: Background information on locally compact groups Locally compact spaces and groups Periodic locally compact groups and their Sylow theory Abelian periodic groups Scalar automorphisms and the mastergraph Inductively monothetic groups Part II: Near abelian groups The definition of near abelian groups Important consequences of the definitions Trivial near abelian groups The class of near abelian groups The Sylow structure of periodic nontrivial near abelian groups and their prime graphs A list of examples Part III: Applications Classifying topologically quasihamiltonian groups Locally compact groups with a modular subgroup lattice Strongly topologically quasihamiltonian groups
Author : R.V. Gamkrelidze
Publisher : Routledge
Page : 544 pages
File Size : 42,7 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351407939
Offering the insights of L.S. Pontryagin, one of the foremost thinkers in modern mathematics, the second volume in this four-volume set examines the nature and processes that make up topological groups. Already hailed as the leading work in this subject for its abundance of examples and its thorough explanations, the text is arranged so that readers can follow the material either sequentially or schematically. Stand-alone chapters cover such topics as topological division rings, linear representations of compact topological groups, and the concept of a lie group.
Author : Dikran N. Dikranjan,Ivan R. Prodanov,Luchezar N. Stoyanov
Publisher : Unknown
Page : 312 pages
File Size : 41,9 Mb
Release : 1990
Category : Mathematics
ISBN : UVA:X001584126
Author : Karl H. Hofmann,Sidney A. Morris
Publisher : Walter de Gruyter GmbH & Co KG
Page : 1076 pages
File Size : 46,6 Mb
Release : 2023-10-23
Category : Mathematics
ISBN : 9783111172606
Author : Markus Stroppel
Publisher : European Mathematical Society
Page : 320 pages
File Size : 40,9 Mb
Release : 2006
Category : Mathematics
ISBN : 3037190167
Locally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter-Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups. The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes.
Author : Deane Montgomery,Leo Zippin
Publisher : Courier Dover Publications
Page : 305 pages
File Size : 41,6 Mb
Release : 2018-06-13
Category : Mathematics
ISBN : 9780486824499
Originally published: New York: Interscience Publishers, Inc., 1955. An unabridged republication of: Huntington, New York: Robert E. Krieger Publishing Company, 1974.
Author : Yevhen G. Zelenyuk
Publisher : Walter de Gruyter
Page : 229 pages
File Size : 42,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110204223
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 22G 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.
Author : Dikran Dikranjan
Publisher : Unknown
Page : 303 pages
File Size : 40,5 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 0598039058
Author : Philip J. Higgins
Publisher : Unknown
Page : 109 pages
File Size : 48,6 Mb
Release : 1974
Category : Topological groups
ISBN : LCCN:10133207
Author : Max Dehn
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461246688
The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as Cayley diagrams), but direct access to his work has been difficult. No edition of his works has been produced, and some of his most important results were never published, at least not by him. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas. It consists of English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere. In addition, I have written a short introduction to each work, summarising its contents and trying to establish its place among related works of Dehn and others, and I have added an appendix on the Dehn-Nielsen theorem (often known simply as Nielsen's theorem) .
