Pontryagin Duality and the Structure of Locally Compact Abelian Groups

Sidney A. Morris

doi:10.1017/CBO9780511600722

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.

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Pontryagin Duality and the Structure of Locally Compact Abelian Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Introduction to topological groups
pp 1-26

2 - Subgroups and quotient groups of Rn
pp 27-40

3 - Uniform spaces and dual groups
pp 41-52

4 - Introduction to the Pontryagin-van Kampen duality theorem
pp 53-61

5 - Duality for compact and discrete groups
pp 62-70

6 - The duality theorem and the principal structure theorem
pp 71-89

7 - Consequences of the duality theorem
pp 90-103

8 - Locally Euclidean and NSS-groups
pp 104-115

9 - Non-abelian groups
pp 116-118

References
pp 119-120

Index of terms
pp 121-126

Index of Exercises, propositions and theorems
pp 127-128

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Pontryagin Duality and the Structure of Locally Compact Abelian Groups

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