Set-Theoretic Topology
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Set-Theoretic Topology

  1. 452 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Set-Theoretic Topology

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Table of contents
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About This Book

Set-Theoretic Topology deals with results concerning set theoretic topology and indicates directions for further investigations. Topics covered include normality and conditions in abstract spaces, compactifications, cardinal invariance, mapping theory, product spaces, and metrization. Comprised of 29 chapters, this volume begins with an example concerning the preservation of the LindelĂśf property in product spaces, followed by a discussion on closed-completeness in spaces with a quasi-G? diagonal and with weak covering properties. The reader is then introduced to countably compact extensions of normal locally compact M-spaces; continuously semi-metrizable spaces; and closed discrete collections of singular cardinality. Subsequent chapters focus on open mapping theory; a selection-theoretic approach to certain extension theorems; semicompletable Moore spaces; and non-normal spaces. The book also considers complete mappings in base of countable order theory before concluding with an analysis of locally separable Moore spaces. This monograph should be of value to students, researchers, and specialists in the field of mathematics.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483263922
Topic
Mathematics
Subtopic
Topology
Index
Mathematics

Table of contents

  1. Front Cover
  2. Set-Theoretic Topology
  3. Copyright Page
  4. Table of Contents
  5. Dedication
  6. CONTRIBUTORS
  7. PREFACE
  8. ACKNOWLEDGMENTS
  9. CHAPTER 1. AN EXAMPLE CONCERNING THE PRESERVATION OF THE LINDELÖF PROPERTY IN PRODUCT SPACES
  10. CHAPTER 2. CLOSED-COMPLETENESS IN SPACES WITH A QUASI-GδDIAGONAL
  11. CHAPTER 3. CLOSED-COMPLETENESS IN SPACES WITH WEAK COVERING PROPERTIES
  12. CHAPTER 4. z-EMBEDDING IN βX x βY
  13. CHAPTER 5. A NOTE ON δθ-REFINABLE SPACES
  14. CHAPTER 6. ON COUNTABLY COMPACT EXTENSIONS OF NORMAL LOCALLY COMPACT M-SPACES
  15. CHAPTER 7. A CHARACTERIZATION OF CONTINUOUSLY SEMIMETRIZABLE SPACES
  16. CHAPTER 8. DENSITY OF COMPACTIFICATIONS
  17. CHAPTER 9. THE PIXLEY-ROY TOPOLOGY ON SPACES OF SUBSETS
  18. CHAPTER 10. SEPARATING CLOSED DISCRETE COLLECTIONS OF SINGULAR CARDINALITY
  19. CHAPTER 11. OPEN MAPPING THEORY
  20. CHAPTER 12. MOORE - CLOSED AND LOCALLY MOORE - CLOSED SPACES
  21. CHAPTER 13. A CONSTRUCTION OF A QUASI-METRIC SOUSLIN SPACE WITH A POINT-COUNTABLE BASE
  22. CHAPTER 14. ON GENERATING NON-ORTHOCOMPACT SPACES
  23. CHAPTER 15. THE ALEXANDROFF-URYSOHN METRIZATION THEOREM REVISITED
  24. CHAPTER 16. THE G(m)-SPACES AND OTHER RELATED TOPICS
  25. CHAPTER 17. STRONG S AND L SPACES UNDER MA
  26. CHAPTER 18. A SELECTION-THEORETIC APPROACH TO CERTAIN EXTENSION THEOREMS
  27. CHAPTER 19. SOME SURPRISING BASE PROPERTIES IN TOPOLOGY II
  28. CHAPTER 20. SOME RESULTS FROM A-SPACES
  29. CHAPTER 21. SOME OBSERVATIONS ON SEMICOMPLETABLE MOORE SPACES
  30. CHAPTER 22. NORMALITY AND SEPARABILITY OF MOORE SPACES
  31. CHAPTER 23. ORTHOCOMPACTNESS IS NORMALITY IN FINITE PRODUCTS OF LOCALLY COMPACT LOTS'S
  32. CHAPTER 24. A REDUCTION OF THE HEREDITARILY SEPARABLE NON-LINDELÖF PROBLEM
  33. CHAPTER 25. FIRST COUNTABLE SPACES WITH CALIBER Ď°1 MAY OR MAY NOT BE SEPARABLE
  34. CHAPTER 26. SOME EXAMPLES CONCERNING Îą-BOUNDED SPACES
  35. CHAPTER 27. NON-NORMAL SPACES
  36. CHAPTER 28. COMPLETE MAPPINGS IN BASE OF COUNTABLE ORDER THEORY
  37. CHAPTER 29. LOCALLY SEPARABLE MOORE SPACES