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

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. 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 Dikran Dikranjan, Anna Giordano Bruno, Lydia Außenhofer. Issued Also In Print. Mode Of Access: Internet Via World Wide Web. In English.