Topological Groups: An IntroductionISBN: 978-0-470-62451-7
Hardcover
367 pages
September 2010
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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.