Pontryagin duality and the structure of locally compact abelian groups / Sidney A. Morris.

Format:

Book

Author/Creator:

Morris, Sidney A., 1947- author.

Series:

London Mathematical Society lecture note series ; 29.

London Mathematical Society lecture note series ; 29

Language:

English

Subjects (All):

Locally compact Abelian groups.

Duality theory (Mathematics).

Pontrjagin duality.

Physical Description:

1 online resource (viii, 128 pages) : digital, PDF file(s).

Other Title:

Pontryagin Duality & the Structure of Locally Compact Abelian Groups

Place of Publication:

Cambridge : Cambridge University Press, 1977.

Language Note:

English

Summary:

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.

Contents:

Cover; Title; Copyright; Contents; Preface; 1. Introduction to topological groups; Exercise set one; Exercise Set Two; Exercise Set Three; Exercise Set Four; 2. Subgroups and quotient groups of Rn; Exercise Set Five; 3. Uniform spaces and dual groups; Exercise Set Six; Exercise Set Seven; 4. Introduction to the Pontryagin-van Kampen duality theorem; Exercise Set Eight; Exercise Set Nine; 5. Duality for compact and discrete groups; Exercise Set Ten; Exercise Set Eleven; 6. The duality theorem and the principal structure theorem; Exercise Set Twelve; Exercise Set Thirteen

7. Consequences of the duality theoremExercise Set Fourteen; Exercise Set Fifteen; 8. Locally Euclidean and NSS-groups; Exercise Set Sixteen; 9. Non-abelian groups; References; Index of terms; Index of Exercises, propositions and theorems

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-139-88373-9

1-107-36578-3

1-107-37051-5

1-107-36087-0

1-107-36931-2

1-299-40359-X

1-107-36332-2

0-511-60072-0