Hewitt-Nachbin spaces

Front Cover......Page 1
Hewitt-Nachbin Spaces......Page 4
Copyright Page......Page 5
TABLE OF CONTENTS......Page 8
PREFACE......Page 6
CHAPTER 1. EMBEDDING IN TOPOLOGICAL PRODUCTS......Page 10
1. Notation and Terminology......Page 14
2. The Embedding Lemma......Page 18
3. Completely Regular Spaces......Page 24
4. E-Compact Spaces......Page 32
5. A Categorical Perspective......Page 41
6. δ-Filters and Convergence......Page 50
7. Hewitt-Nachbin Completeness via Ideals, Filters, and Nets......Page 67
8. Characterizations and Properties of Hewitt-Nachbin Spaces......Page 83
9. Hewitt-Nachbin Completions......Page 105
10. z-Embedding and u-Embedding......Page 117
11. Hewitt-Nachbin Completions of Products......Page 129
CHAPTER 3. HEWITT-NACHBIN SPACES, UNIFORMITIES, AND RELATED TOPOLOGICAL SPACES......Page 145
12. A Review of Uniform Spaces......Page 146
13. Hewitt-Nachbin Completeness and Uniform Spaces......Page 152
14. Almost Realcompact and cb-Spaces......Page 166
CHAPTER 4. HEWITT- NACHBIN COMPLETENESS AND CONTINUOUS MAPPINGS......Page 180
15. Some Classes of Mappings......Page 182
16. Perfect Mappings......Page 195
17. Closed Mappings and Hewitt-Nachbin Spaces......Page 207
18. WZ-Mappings......Page 222
19. E-Perfect Mappings......Page 234
BIBLIOGRAPHY......Page 246
INDEX......Page 270