Topological Groups and Related Structures

Topological Groups and Related Structures
Title Topological Groups and Related Structures PDF eBook
Author A. V. Arkhangelʹskiĭ
Publisher atlantis press
Pages 797
Release 2008
Genre Mathematics
ISBN 9078677066

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This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology.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.

Topological Groups and Related Structures, An Introduction to Topological Algebra.

Topological Groups and Related Structures, An Introduction to Topological Algebra.
Title Topological Groups and Related Structures, An Introduction to Topological Algebra. PDF eBook
Author Alexander Arhangel’skii
Publisher Springer Science & Business Media
Pages 794
Release 2008-05-01
Genre Mathematics
ISBN 949121635X

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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.

Introduction to Topological Groups

Introduction to Topological Groups
Title Introduction to Topological Groups PDF eBook
Author Taqdir Husain
Publisher Courier Dover Publications
Pages 241
Release 2018-02-15
Genre Mathematics
ISBN 0486819191

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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.

A Physicists Introduction to Algebraic Structures

A Physicists Introduction to Algebraic Structures
Title A Physicists Introduction to Algebraic Structures PDF eBook
Author Palash B. Pal
Publisher Cambridge University Press
Pages 717
Release 2019-05-23
Genre Mathematics
ISBN 1108492207

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Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.

A Concise Course in Algebraic Topology

A Concise Course in Algebraic Topology
Title A Concise Course in Algebraic Topology PDF eBook
Author J. P. May
Publisher University of Chicago Press
Pages 262
Release 1999-09
Genre Mathematics
ISBN 9780226511832

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Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Algebraic Topology: A Structural Introduction

Algebraic Topology: A Structural Introduction
Title Algebraic Topology: A Structural Introduction PDF eBook
Author Marco Grandis
Publisher World Scientific Publishing Company
Pages 370
Release 2021-12-24
Genre Mathematics
ISBN 9789811248351

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Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation. This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites - basic general topology and little else - and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions. It can be used as a textbook for a semester course or self-study, and a guidebook for further study.

Coarse Geometry of Topological Groups

Coarse Geometry of Topological Groups
Title Coarse Geometry of Topological Groups PDF eBook
Author Christian Rosendal
Publisher Cambridge University Press
Pages 309
Release 2021-12-16
Genre Mathematics
ISBN 110884247X

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