Pontryagin Duality and the Structure of

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.

Introduction to topological groups
Subgroups and quotient groups of Rn
Uniform spaces and dual groups
Introduction to the Pontryagin-van Kampen duality theorem
Duality for compact and discrete groups
The duality theorem and the principal structure theorem
Consequences of the duality theorem
Locally Euclidean and NSS-groups
Non-abelian groups
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Pontryagin Duality and the Structure of Locally Compact Abelian Groups

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