Compactness Conditions For Functions On Topological Groups
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Compactness Conditions For Functions On Topological Groups
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Author : Justin Randolph Peters
language : en
Publisher:
Release Date : 1972
Compactness Conditions For Functions On Topological Groups written by Justin Randolph Peters and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 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.
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 Groups And Related Structures An Introduction To Topological Algebra
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Author : Alexander Arhangel’skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-01
Topological Groups And Related Structures An Introduction To Topological Algebra written by Alexander Arhangel’skii 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 2008-05-01 with Mathematics categories.
Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
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.
Introduction To Topological Groups
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Author : Taqdir Husain
language : en
Publisher: Courier Dover Publications
Release Date : 2018-02-15
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 2018-02-15 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.
Extensions Of Positive Definite Functions
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Author : John R. McMullen
language : en
Publisher: American Mathematical Soc.
Release Date : 1972
Extensions Of Positive Definite Functions written by John R. McMullen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Recent Progress In General Topology Ii
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Author : M. Husek
language : en
Publisher: Elsevier
Release Date : 2002-11-13
Recent Progress In General Topology Ii written by M. Husek and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-13 with Mathematics categories.
The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade. It follows freelythe previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared inconnection with the Prague Topological Symposium, held in 2001. During the last 10 years the focusin General Topology changed and therefore the selection of topics differs slightly from thosechosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (includingInfinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as:R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
Probability Measures On Locally Compact Groups
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Author : H. Heyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability Measures On Locally Compact Groups written by H. Heyer 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.
Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.
Banach Algebras And Their Applications
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Author : Anthony To-Ming Lau
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Banach Algebras And Their Applications written by Anthony To-Ming Lau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from - theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.