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Counterexamples in topology 拓扑学中的反例

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Counterexamples in topology 拓扑学中的反例

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作 者:LynnArthurSteen 著

出 版 社:Oversea Publishing House

出版时间:1995-9-1

I S B N:9780486687353

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内容简介

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.

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目录

Part I BASIC DEFINITIONS
 1. General Introduction
  Limit Points
  Closures and Interiors
  Countability Properties
  Functions
  Filters
 2. Separation Axioms
  Regular and Normal Spaces
  Completely Hausdorff Spaces
  Completely Regular Spaces
  Functions, Products, and Subspaces
  Additional Separation Properties
 3. Compactness
  Global Compactness Properties
  Localized Compactness Properties
  Countability Axioms and Separability
  Paracompactness
  Compactness Properties and Tl Axioms
  Invariance Properties
 4. Connectedness
  Functions and Products
  Disconnectedness
  Biconnectedness and Continua
 5. Metric Spaces
  Complete Metric Spaces
  Metrizability
  Uniformities
  Metric Uniformities
Part II COUNTEREXAMPLES
 1. Finite Discrete Topology
 2. Countable Discrete Topology
 3. Uncountable Discrete Topology
 4. Indiscrete Topology
 5. Partition Topology
 6. Odd-Even Topology
 7. Deleted Integer Topology
 8. Finite Particular Point Topology
 9. Countable Particular Point Topology
 10. Uncountable Particular Point Topology
 11. Sierpinski Space
 12. Closed Extension Topology
 13. Finite Excluded Point Topology
 14. Countable Excluded Point Topology
 15. Uncountable Excluded Point Topology
 16. Open Extension Topology 47
 17. Either-Or Topology 48
 18. Finite Complement Topology on a Countable Space
 19. Finite Complement Topology on an Uncountable Space
 20. Countable Complement Topology
 21. Double Pointed Countable Complement Topology
 22. Compact Complement Topology
 23. Countable Fort Space
 24. Uncountable Fort Space
 25. Fortissimo Space
 26. Arens-Fort Space
 27. Modified Fort Space
 28. Euclidean Topology
 29. The Cantor Set
 30. The Rational Numbers
 31. The Irrational Numbers
 32. Special Subsets of the Real Line
 33. Special Subsets of the Plane
 34. One Point Compactification Topology
……
Part III METRIZATION THEORY
Part IV APPENDICES
General Reference Chart
Problems
Notes
Bibligraphy

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