Topological Groups and the Pontryagin-van Kampen Duality: An Introduction

Lydia Außenhofer; Dikran Dikranjan; Anna Giordano Bruno

Published by De Gruyter 2022

Topological Groups and the Pontryagin-van Kampen Duality

An Introduction

Lydia Außenhofer , Dikran Dikranjan and Anna Giordano Bruno

Volume 83 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110654936

Overview
Contents

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

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	IX
1 Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2 Definition and examples Requires Authentication Unlicensed Licensed Download PDF	7
3 General properties of topological groups Requires Authentication Unlicensed Licensed Download PDF	27
4 Markov’s problems Requires Authentication Unlicensed Licensed Download PDF	51
5 Cardinal invariants and metrizability Requires Authentication Unlicensed Licensed Download PDF	67
6 Connectedness in topological groups Requires Authentication Unlicensed Licensed Download PDF	91
7 Completeness and completion Requires Authentication Unlicensed Licensed Download PDF	97
8 Compactness and local compactness – a first encounter Requires Authentication Unlicensed Licensed Download PDF	115
9 Properties of ℝⁿ and its subgroups Requires Authentication Unlicensed Licensed Download PDF	131
10 Subgroups of compact groups Requires Authentication Unlicensed Licensed Download PDF	143
11 The Følner theorem Requires Authentication Unlicensed Licensed Download PDF	159
12 Almost periodic functions and Haar integrals Requires Authentication Unlicensed Licensed Download PDF	187
13 The Pontryagin-van Kampen duality Requires Authentication Unlicensed Licensed Download PDF	201
14 Applications of the duality theorem Requires Authentication Unlicensed Licensed Download PDF	229
15 Pseudocompact groups Requires Authentication Unlicensed Licensed Download PDF	263
16 Topological rings, fields, and modules Requires Authentication Unlicensed Licensed Download PDF	275
A Background on groups Requires Authentication Unlicensed Licensed Download PDF	291
B Background on topological spaces Requires Authentication Unlicensed Licensed Download PDF	315
C Background on categories and functors Requires Authentication Unlicensed Licensed Download PDF	341
Bibliography Requires Authentication Unlicensed Licensed Download PDF	357
Index of symbols Requires Authentication Unlicensed Licensed Download PDF	369
Index Requires Authentication Unlicensed Licensed Download PDF	371

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate students and researchers in mathematics.
Pages
- Front matter: 14
- Main content: 378
Keywords: Lokal kompakte Abelsche Gruppe; Pontrjagin-Dualität; Topologische Gruppe

eBook

Published: November 22, 2021
ISBN: 9783110654936

Hardcover

Published: November 22, 2021
ISBN: 9783110653496