Topological Groups And Related Structures

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Topological Groups And Related Structures

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Author : A. V. Arkhangelʹskiĭ
language : en
Publisher: atlantis press
Release Date : 2008

Topological Groups And Related Structures written by A. V. Arkhangelʹskiĭ and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short -- almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.

Ultrafilters And Topologies On Groups

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Author : Yevhen G. Zelenyuk
language : en
Publisher: Walter de Gruyter
Release Date : 2011

Ultrafilters And Topologies On Groups written by Yevhen G. Zelenyuk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

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.

Introduction To Topological Groups

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Author : Taqdir Husain
language : en
Publisher: Courier Dover Publications
Release Date : 2018-01-10

Introduction To Topological Groups written by Taqdir Husain and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-10 with Mathematics categories.

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.

Topological Groups

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Author : Sidney A. Morris
language : en
Publisher: MDPI
Release Date : 2019-03-05

Topological Groups written by Sidney A. Morris and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-05 with Mathematics categories.

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.

Coarse Geometry Of Topological Groups

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Author : Christian Rosendal
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16

Coarse Geometry Of Topological Groups written by Christian Rosendal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Mathematics categories.

Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.

Topological Groups And The Pontryagin Van Kampen Duality

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Author : Lydia Außenhofer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22

Topological Groups And The Pontryagin Van Kampen Duality written by Lydia Außenhofer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.

This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.

Topological Groups

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Author : R. V. Gamkrelidze
language : en
Publisher: CRC Press
Release Date : 1987-03-06

Topological Groups written by R. V. Gamkrelidze and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-06 with Mathematics categories.

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.

Convergence Structures And Applications To Functional Analysis

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Author : R. Beattie
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Convergence Structures And Applications To Functional Analysis written by R. Beattie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus. The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological groups and topological vector spaces. Readers will find the text rich in examples. Of interest, as well, are the many filter and ultrafilter proofs which often provide a fresh perspective on a well-known result. Audience: This text will be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.

Topological Groups Yesterday Today Tomorrow

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Author : Sidney A. Morris
language : en
Publisher: MDPI
Release Date : 2018-09-27

Topological Groups Yesterday Today Tomorrow written by Sidney A. Morris and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Mathematics categories.

This book is a printed edition of the Special Issue "Topological Groups: Yesterday, Today, Tomorrow" that was published in Axioms

Pseudocompact Topological Spaces

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Author : Michael Hrušák
language : en
Publisher: Springer
Release Date : 2018-07-19

Pseudocompact Topological Spaces written by Michael Hrušák and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Mathematics categories.

This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.