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Topological Groups and the Pontryagin-van Kampen Duality
An Introduction
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Lydia Außenhofer
Language:
English
Published/Copyright:
2022
About this book
This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.
- A carefully-written introduction to topological groups
- Treats the structure theory of locally compact abelian groups
- Puts an emphasis on Pontryagin-van Kampen duality
Author / Editor information
Lydia Außenhofer, University of Passau, Germany; Dikran Dikranjan and Anna Giordano Bruno, University of Udine, Italy.
Reviews
"[...] All in all, this book achieves two main goals, it can be used as a complete introduction to the theory of topological groups, but it also provides the more advanced reader with the powerful techniques developed around the duality theory of locally compact abelian groups and its many applications. Thus, this work is a worthy successor of the celebrated monograph written by Dikranjan, Prodanov, and Stoyanov and therefore highly recommended to all people interested in the study of topological groups."
Prof. Salvador Hernández-Muñoz, Universitat Jaume I, Spain, February 2022
Topics
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Frontmatter
I -
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Preface
V -
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Contents
IX -
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1 Introduction
1 -
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2 Definition and examples
7 -
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3 General properties of topological groups
27 -
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4 Markov’s problems
51 -
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5 Cardinal invariants and metrizability
67 -
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6 Connectedness in topological groups
91 -
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7 Completeness and completion
97 -
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8 Compactness and local compactness – a first encounter
115 -
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9 Properties of ℝn and its subgroups
131 -
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10 Subgroups of compact groups
143 -
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11 The Følner theorem
159 -
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12 Almost periodic functions and Haar integrals
187 -
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13 The Pontryagin-van Kampen duality
201 -
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14 Applications of the duality theorem
229 -
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15 Pseudocompact groups
263 -
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16 Topological rings, fields, and modules
275 -
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A Background on groups
291 -
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B Background on topological spaces
315 -
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C Background on categories and functors
341 -
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Bibliography
357 -
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Index of symbols
369 -
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Index
371
Publishing information
Pages and Images/Illustrations in book
eBook published on:
November 22, 2021
eBook ISBN:
9783110654936
Hardcover published on:
November 22, 2021
Hardcover ISBN:
9783110653496
Pages and Images/Illustrations in book
Front matter:
14
Main content:
378
Audience(s) for this book
Graduate students and researchers in mathematics.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
