Algebraic Structure Of Pseudocompact Groups
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Algebraic Structure Of Pseudocompact Groups
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Author : Dikran N. Dikranjan
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Algebraic Structure Of Pseudocompact Groups written by Dikran N. Dikranjan 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 1998 with Mathematics categories.
The fundamental property of compact spaces - that continuous functions defined on compact spaces are bounded - served as a motivation for E. Hewitt to introduce the notion of a pseudocompact space. The class of pseudocompact spaces proved to be of fundamental importance in set-theoretic topology and its applications. This clear and self-contained exposition offers a comprehensive treatment of the question, When does a group admit an introduction of a pseudocompact Hausdorff topology that makes group operations continuous? Equivalently, what is the algebraic structure of a pseudocompact Hausdorff group? The authors have adopted a unifying approach that covers all known results and leads to new ones, Results in the book are free of any additional set-theoretic assumptions.
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.
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.
N Algebraic Structures
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2005-01-01
N Algebraic Structures written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
In this book, for the first time we introduce the notions of N-groups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, N-loops and Smarandache N-loops are introduced and analyzed. Chapter four defines N-groupoids and S-N-groupoids. Since the N-semigroup structures are sandwiched between groups and groupoids, the study can be carried out without any difficulty. Mixed N-algebraic structures and S-mixed algebraic structures are given in chapter five. Some problems are suggested in chapter six. It is pertinent to mention that several exercises and problems (Some in the form of proof to the theorems are given in all the chapters.) A reader who attempts to solve them will certainly gain a sound knowledge about these concepts. We have given 50 problems for the reader to solve in chapter 6. The main aim of this book is to introduce new concepts and explain them with examples there by encouraging young mathematics to pursue research in this direction. Several theorems based on the definition can be easily proved with simple modification. Innovative readers can take up that job. Also these notions find their applications in automaton theory and coloring problems. The N-semigroups and N-automaton can be applied to construct finite machines, which can perform multitasks, so their capability would be much higher than the usual automaton of finite machines constructed. We have suggested a list of references for further reading.
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.
Open Problems In Topology Ii
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Author : Elliott M. Pearl
language : en
Publisher: Elsevier
Release Date : 2011-08-11
Open Problems In Topology Ii written by Elliott M. Pearl and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world
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.
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 of General Topology and its applications to Algebra and Analysis during the last decade. It follows freely the 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 in connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-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.
Abelian Groups Rings And Modules
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Author : Andrei V. Kelarev
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Abelian Groups Rings And Modules written by Andrei V. Kelarev 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 2001 with Mathematics categories.
This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a few specially invited papers. The proceedings were dedicated to Professor László Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce. Four surveys from leading experts follow Professor Salce's article. They present recent results from active research areas
Groups 93 Galway St Andrews Volume 1
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Author : C. M. Campbell
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-16
Groups 93 Galway St Andrews Volume 1 written by C. M. Campbell 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 1995-03-16 with Mathematics categories.
Representing the wealth and diversity of group theory for experienced researchers as well as new postgraduates, this two-volume book contains selected papers from the international conference which was held at University College Galway in August 1993.