Topological Groups An Introduction

Edition: 1st
Format: Hardcover
Pub. Date: 2010-09-22
Publisher(s): Wiley
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Written by an avid user of topological groups, this book provides a concrete introduction to metric and topological groups. Important metric spaces are first introduced with the construction of a concrete metric, and a topological characterization of their open sets is immediately established. Many proofs are presented in a purely topological fashion. It is this use of topologies that affords the opportunity to discuss the limitations of some of the metric group results as well as the topological machinery needed to generalize them. The book focuses on metric cases, thus keeping many proofs in familiar territory for readers new to the topic. 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. When used in proofs, the calculations, remarks, and facts are carefully referred to so that advanced readers will know what is needed in the proof and will be able to move forward at a faster pace. Novice readers will have to reference the exercise and workout a solution to become more engaged with the material.

Author Biography

Nelson G. Markley, PhD, was professor of mathematics at the University of Maryland for more than twenty-five years and also served as provost at Lehigh University. He has written numerous journal articles in the area of dynamical systems and is the author of Principles of Differential Equations, also published by Wiley.

Table of Contents

Groups and Metrics
Metric and Topological Spaces
Continuous Group Operations
Subgroups and Their Quotient Spaces
Compactness and Metric Groups
Linear Spaces and Algebras
Linear Structures on Groups
Linear Functions
Norms on Linear Spaces
Continuous Linear Functions
The Determinant Function
The Subgroups of Rn
Closed Subgroups
Quotient Groups
Dense Subgroups
Matrix Groups
General Linear Groups
Orthogonal and Unitary Groups
Triangular Groups
One-Parameter Subgroups
Connectedness of Topological Groups
Connected Topological Spaces
Connected Matrix Groups
Compact Product Spaces
Totally Disconnected Groups
Metric Groups of Functions
Real-Valued Functions
The Compact-Open Topology
Metric Groups of Isometries
Metric Groups of Homeomorphisms
Metric Groups of Homomorphisms
Compact Groups
Invariant Means
Integral Equations
Compact Abelian Groups
Matrix Representations
Character Groups
Countable Discrete Abelian Groups
The Duality Homomorphism
Compactly Generated Abelian Groups
A Duality Theorem
Index of Special Symbols
Table of Contents provided by Publisher. All Rights Reserved.

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