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Topological groups: an introduction

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Bibliographic Details
Main Author:	Markley, Nelson Groh 1940- (Author)
Format:	Book
Language:	English
Published:	Hoboken, NJ Wiley 2010
Subjects:	Topological groups Topologische Gruppe Lehrbuch
Online Access:	Inhaltsverzeichnis Klappentext
Physical Description:	XI, 367 S.
ISBN:	9780470624517

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MARC


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adam_text	Contents Preface ix Groups and Topologies 1 1.1 Groups ................................. 2 1.2 Metric and Topological Spaces ................... 13 1.3 Continuous Group Operations .................... 29 1.4 Subgroups and Their Quotient Spaces ............... 40 1.5 Compactness and Metric Groups .................. 51 Linear Spaces and Algebras 63 2.1 Linear Structures on Groups .................... 64 2.2 Linear Functions ........................... 70 2.3 Norms on Linear Spaces ....................... 83 2.4 Continuous Linear Functions .................... 92 2.5 The Determinant Function ...................... 99 The Subgroups of W1 115 3.1 Closed Subgroups ...........................116 3.2 Quotient Groups ...........................125 3.3 Dense Subgroups ...........................132 Matrix Groups 140 4.1 General Linear Groups ........................141 4.2 Orthogonal and Unitary Groups ..................149 4.3 Triangular Groups ..........................159 4.4 One-Parameter Subgroups ......................169 Connectedness of Topological Groups 181 5.1 Connected Topological Spaces ....................182 5.2 Connected Matrix Groups ......................193 5.3 Compact Product Spaces ......................207 5.4 Totally Disconnected Groups ....................214 vii viii CONTENTS 6 Metric Groups of Functions 223 6.1 Real-Valued Functions ........................224 6.2 The Compact-Open Topology ....................233 6.3 Metric Groups of Isometries .....................243 6.4 Metric Groups of Homeomorphisms .................248 6.5 Metric Groups of Homomorphisms .................255 7 Compact Groups 262 7.1 Invariant Means ...........................263 7.2 Integral Equations ..........................274 7.3 Eigenfunctions ............................292 7.4 Compact Abelian Groups ......................302 7.5 Matrix Representations .......................310 8 Character Groups 319 8.1 Countable Discrete Abelian Groups .................320 8.2 The Duality Homomorphism ....................329 8.3 Compactly Generated Abelian Groups ...............337 8.4 A Duality Theorem ..... .....................344 Bibliography 359 Index of Special Symbols 362 Index 364 чшіу introduction to metric ar Topological Groups: An Introduction provides a self-contained presentation with an emphasis on important families of topological groups. The book uniquely provides a modern and balanced presentation by using metric groups to present a substantive introduction to topics such as duality, while also shedding light on more general results for topological groups. Filling the need for a broad and accessible introduction to the subject, the book be¬ gins with coverage of groups, metric spaces, and topological spaces before introduc¬ ing topological groups. Since linear spaces, algebras, norms, and determinants are necessary tools for studying topological groups, their basic properties are developed in subsequent chapters. For concreteness, product topologies, quotient topologies, and compact-open topologies are first introduced as metric spaces before their open sets are characterized by topological properties. These metrics, along with invariant metrics, act as excellent stepping stones to the subsequent discussions of the following topics: • Matrix groups s Connectednesss of topological groups • Compact groups Character groups Exercises found throughout the book are designed so both novice and advanced read¬ ers will be able to work out solutions and move forward at their desired pace. All chapters include a variety of calculations, remarks, and elementary results, which are incorporated into the various examples and exercises. Topologicul Groups: An Introduction is an excellent book for advanced undergraduate and graduate-level courses on the topic. The book also serves as a valuable resource for professionals working in the fields of mathematics, science, engineering, and physics. was professor of mathematics at the University of Maryland for more than twenty-five years and also served as provost at Lehigh Univer¬ sity. He has written numerous journal articles in the area of dynamical systems and is the author of Principies of Differential Equations, also published by Wiley. Ψ WILEY wiiev.com ISBN 476-0-470^5451-7 90000 9 780470ll624517l
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title	Topological groups an introduction
title_auth	Topological groups an introduction
title_exact_search	Topological groups an introduction
title_full	Topological groups an introduction Nelson G. Markley
title_fullStr	Topological groups an introduction Nelson G. Markley
title_full_unstemmed	Topological groups an introduction Nelson G. Markley
title_short	Topological groups
title_sort	topological groups an introduction
title_sub	an introduction
topic	Topological groups Topologische Gruppe (DE-588)4135793-0 gnd
topic_facet	Topological groups Topologische Gruppe Lehrbuch
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