Contents
Introduction xiii
Acknowledgments xv
Notational Conventions xv
Par t 1.
GENERAL THEORY OF TOPOLOGICAL GROUPS
Chapter 1. Basic Topological Group Theory 3
1.1. Definition and Separation Properties 3
1.2. Subgroups, Quotient Groups, and Quotient Spaces 4
1.3. Connectedness 5
1.4. Covering Groups 7
1.5. Transformation Groups and Homogeneous Spaces 8
1.6. The Locally Compact Case 9
1.7. Product Groups 12
1.8. Invariant Metrics on Topological Groups 15
Chapter 2. Some Examples 19
2.1. General and Special Linear Groups 19
2.2. Linear Lie Groups 20
2.3. Groups Defined by Bilinear Forms 21
2.4. Groups Defined by Hermitian Forms 22
2.5. Degenerate Forms 25
2.6. Automorphism Groups of Algebras 26
2.7. Spheres, Projective Spaces and Grassmannians 28
2.8. Complexification of Real Groups 30
2.9. p-adic Groups 32
2.10. Heisenberg Groups 33
Chapter 3. Integration and Convolution 35
3.1. Definition and Examples 35
3.2. Existence and Uniqueness of Haar Measure 36
3.3. The Modular Function 41
3.4. Integration on Homogeneous Spaces 44
3.5. Convolution and the Lebesgue Spaces 45
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