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

Topological Groups and the Pontryagin-van Kampen Duality : : An Introduction / / Dikran Dikranjan, Anna Giordano Bruno, Lydia Außenhofer.

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 tr...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
VerfasserIn:
Außenhofer, Lydia,
Dikranjan, Dikran,
Giordano Bruno, Anna,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2021]
©2022
Year of Publication:2021
Language:English
Series:De Gruyter Studies in Mathematics , 83
Online Access:
Physical Description:1 online resource (XIV, 378 p.)
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Table of Contents:
  • Frontmatter
  • Preface
  • Contents
  • 1 Introduction
  • 2 Definition and examples
  • 3 General properties of topological groups
  • 4 Markov’s problems
  • 5 Cardinal invariants and metrizability
  • 6 Connectedness in topological groups
  • 7 Completeness and completion
  • 8 Compactness and local compactness – a first encounter
  • 9 Properties of ℝn and its subgroups
  • 10 Subgroups of compact groups
  • 11 The Følner theorem
  • 12 Almost periodic functions and Haar integrals
  • 13 The Pontryagin-van Kampen duality
  • 14 Applications of the duality theorem
  • 15 Pseudocompact groups
  • 16 Topological rings, fields, and modules
  • A Background on groups
  • B Background on topological spaces
  • C Background on categories and functors
  • Bibliography
  • Index of symbols
  • Index

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