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Markley, Nelson G.
Topological Groups
An Introduction

1. Edition October 2010
89.90 Euro
2010. 368 Pages, Hardcover
ISBN 978-0-470-62451-7 - John Wiley & Sons




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Short description
Written by an avid user of topological groups, this book provides a concrete introduction to metric and topological groups. Readers learn how to replace the sequences with nets to obtain a general proof, and the result is an increased emphasis on topological groups and less on general topology. The exercises have been designed to help hold the interest of advanced and beginning readers, and a variety of calculations, remarks, and necessary related facts have been placed within the exercises and are used throughout the text.

From the contents
Preface.

1 Groups and Metrics.

1.1 Groups.

1.2 Metric and Topological Spaces.

1.3 Continuous Group Operations.

1.4 Subgroups and Their Quotient Spaces.

1.5 Compactness and Metric Groups.

2 Linear Spaces and Algebras.

2.1 Linear Structures on Groups.

2.2 Linear Functions.

2.3 Norms on Linear Spaces.

2.4 Continuous Linear Functions.

2.5 The Determinant Function.

3 The Subgroups of Rn.

3.1 Closed Subgroups.

3.2 Quotient Groups.

3.3 Dense Subgroups.

4 Matrix Groups.

4.1 General Linear Groups.

4.2 Orthogonal and Unitary Groups.

4.3 Triangular Groups.

4.4 One-Parameter Subgroups.

5 Connectedness of Topological Groups.

5.1 Connected Topological Spaces.

5.2 Connected Matrix Groups.

5.3 Compact Product Spaces.

5.4 Totally Disconnected Groups.

6 Metric Groups of Functions.

6.1 Real-Valued Functions.

6.2 The Compact-Open Topology.

6.3 Metric Groups of Isometries.

6.4 Metric Groups of Homeomorphisms.

6.5 Metric Groups of Homomorphisms.

7 Compact Groups.

7.1 Invariant Means.

7.2 Integral Equations.

7.3 Eigenfunctions.

7.4 Compact Abelian Groups.

7.5 Matrix Representations.

8 Character Groups.

8.1 Countable Discrete Abelian Groups.

8.2 The Duality Homomorphism.

8.3 Compactly Generated Abelian Groups.

8.4 A Duality Theorem.

Bibliography.

Index of Special Symbols.

Index.

 





 

        

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