Compactness Conditions In Structure Theory Of Topological Groups
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Compactness Conditions In Structure Theory Of Topological Groups
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Author : Siegfried Karl Grosser
language : en
Publisher:
Release Date : 1965
Compactness Conditions In Structure Theory Of Topological Groups written by Siegfried Karl Grosser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.
Topological Rings Satisfying Compactness Conditions
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Author : M. Ursul
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Rings Satisfying Compactness Conditions written by M. Ursul 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 2012-12-06 with Mathematics categories.
Introduction In the last few years a few monographs dedicated to the theory of topolog ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings. The theory of Banach algebras uses results of Banach spaces, and the theory of locally compact rings uses the theory of LCA groups. As far as the author knows, the first papers on the theory of locally compact rings were [Pontr1]' [J1], [J2], [JT], [An], lOt], [K1]' [K2]' [K3], [K4], [K5], [K6]. Later two papers, [GS1,GS2]appeared, which contain many results concerning locally compact rings. This book can be used in two w.ays. It contains all necessary elementary results from the theory of topological groups and rings. In order to read these parts of the book the reader needs to know only elementary facts from the theories of groups, rings, modules, topology. The book consists of two parts.
The Structure Of Compact Groups
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Author : Karl H. Hofmann
language : en
Publisher: Walter de Gruyter
Release Date : 2013-08-29
The Structure Of Compact Groups written by Karl H. Hofmann 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 2013-08-29 with Mathematics categories.
The subject matter of compact groups is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics. This book serves the dual purpose of providing a textbook on it for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups, on compact Lie groups, and on locally compact abelian groups. Separate appended chapters contain the material for courses on abelian groups and on category theory. However, the thrust of the book points in the direction of the structure theory of not necessarily finite dimensional, nor necessarily commutative, compact groups, unfettered by weight restrictions or dimensional bounds. In the process it utilizes infinite dimensional Lie algebras and the exponential function of arbitrary compact groups. The first edition of 1998 and the second edition of 2006 were well received by reviewers and have been frequently quoted in the areas of instruction and research. For the present new edition the text has been cleaned of typographical flaws and the content has been conceptually sharpened in some places and polished and improved in others. New material has been added to various sections taking into account the progress of research on compact groups both by the authors and other writers. Motivation was provided, among other things, by questions about the structure of compact groups put to the authors by readers through the years following the earlier editions. Accordingly, the authors wished to clarify some aspects of the book which they felt needed improvement. The list of references has increased as the authors included recent publications pertinent to the content of the book.
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.
The Structure Of Compact Groups
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Author : Karl H. Hofmann
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-06-08
The Structure Of Compact Groups written by Karl H. Hofmann 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 2020-06-08 with Mathematics categories.
This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.
Locally Compact Groups
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Author : Markus Stroppel
language : en
Publisher: European Mathematical Society
Release Date : 2006
Locally Compact Groups written by Markus Stroppel and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Periodic Locally Compact Groups
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Author : Wolfgang Herfort
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-19
Periodic Locally Compact Groups written by Wolfgang Herfort 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 2018-11-19 with Mathematics categories.
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
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.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
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.
Compactness Conditions And Duals Of Topological Groups
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Author : John Robie Liukkonen
language : en
Publisher:
Release Date : 1970
Compactness Conditions And Duals Of Topological Groups written by John Robie Liukkonen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Topological groups categories.
