Counterexamples in Topology(Dover Books on Mathematics)

Counterexamples in Topology(Dover Books on Mathematics)
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作者: , ,
1995-09
版次: 1
ISBN: 9780486687353
定价: 127.70
装帧: 平装
开本: 其他
纸张: 胶版纸
页数: 272页
正文语种: 英语
1人买过
  • Over140examples,precededbyasuccinctexpositionofgeneraltopologyandbasicterminology.Eachexampletreatedasawhole.Over25Venndiagramsandchartssummarizepropertiesoftheexamples,whilediscussionsofgeneralmethodsofconstructionandchangegivereadersinsightintoconstructingcounterexamples.Includesproblemsandexercises,correlatedwithexamples.Bibliography.1978edition. 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
  • 内容简介:
    Over140examples,precededbyasuccinctexpositionofgeneraltopologyandbasicterminology.Eachexampletreatedasawhole.Over25Venndiagramsandchartssummarizepropertiesoftheexamples,whilediscussionsofgeneralmethodsofconstructionandchangegivereadersinsightintoconstructingcounterexamples.Includesproblemsandexercises,correlatedwithexamples.Bibliography.1978edition.
  • 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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