Pontryagin Duality and the Structure of Locally Compact Abelian Groups [Paperback]

These lecture notes begin with an introduction to topological groups.These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required.These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required.These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.1. Introduction to topological groups; 2. Subgroups and quotient groups of Rn; 3. Uniform spaces and dual groups; 4. Introduction to the Pontryagin-van Kampen duality theorem; 5. Duality for compact and discrete groups; 6. The duality theorem and the principal structure theorem; 7. Consequences of the duality theorem; 8. Locally Euclidean and NSS-groups; 9. Non-abelian groups.