Topological groups: an introduction

Abstract

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.