Topology and Normed Spaces 0470439246, 1948977982

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Table of contents :
Front Cover......Page 1
Title Page......Page 4
Copyright Information......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 10
Notation and conventions......Page 14
Dependence chart......Page 15
Part I: Topology......Page 18
1. Basic concepts......Page 18
2. Metric and normed spaces......Page 31
3. Further elementary theory......Page 45
4. Separation properties......Page 56
5. Connected spaces......Page 64
6. Bases of neighbourhoods and open sets; countability axioms......Page 70
7. Finite products......Page 78
8. Complete metric spaces......Page 84
9. Compactness......Page 99
10. Properties related to compactness......Page 113
11. Compact and totally bounded metric spaces......Page 121
12. Existence of continuous real functions......Page 128
13. More about connectedness......Page 143
14. Infinite products......Page 150
15. The Cantor space......Page 158
Part II: Normed Linear Spaces......Page 165
16. Elementary theory......Page 165
17. Some particular spaces......Page 175
18. Linear mappings......Page 185
19. Linear functional......Page 204
20. Finite-dimensional spaces......Page 212
21. Convexity......Page 220
22. Convex series, closed-graph theorems......Page 229
23. Extension and separation theorems......Page 239
24. Dual spaces......Page 254
25. Constructions giving new spaces......Page 265
26. Spaces of continuous functions......Page 278
27. Weak topologies......Page 297
28. Tychonoff's theorem and its applications......Page 312
29. Complemented subspaces......Page 322
30. Bases......Page 339
31. Unconditional convergence......Page 357
32. Hilbert spaces......Page 369
33. Linear lattices......Page 381
34. Compact linear mappings......Page 393
35. The duality of pairs of subspaces......Page 404
Appendix 1: Countability......Page 409
Appendix 2: Zorn's lemma......Page 413
Symbols introduced in the text......Page 417
Bibliography......Page 419
Index......Page 422

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