7 Completeness and completion

Kapitel in diesem Buch

1. Frontmatter I
2. Preface V
3. Contents IX
4. 1 Introduction 1
5. 2 Definition and examples 7
6. 3 General properties of topological groups 27
7. 4 Markov’s problems 51
8. 5 Cardinal invariants and metrizability 67
9. 6 Connectedness in topological groups 91
10. 7 Completeness and completion 97
11. 8 Compactness and local compactness – a first encounter 115
12. 9 Properties of ℝⁿ and its subgroups 131
13. 10 Subgroups of compact groups 143
14. 11 The Følner theorem 159
15. 12 Almost periodic functions and Haar integrals 187
16. 13 The Pontryagin-van Kampen duality 201
17. 14 Applications of the duality theorem 229
18. 15 Pseudocompact groups 263
19. 16 Topological rings, fields, and modules 275
20. A Background on groups 291
21. B Background on topological spaces 315
22. C Background on categories and functors 341
23. Bibliography 357
24. Index of symbols 369
25. Index 371