A first course in algebraic topology

書誌事項

A first course in algebraic topology

Czes Kosniowski

Cambridge University Press, 1980

  • pbk.

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注記

Bibliography: p. [260]-261

Includes index

内容説明・目次

内容説明

This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.

目次

  • Preface
  • Sets and groups
  • 1. Background: metric spaces
  • 2. Topological spaces
  • 3. Continuous functions
  • 4. Induced topology
  • 5. Quotient topology (and groups acting on spaces)
  • 6. Product spaces
  • 7. Compact spaces
  • 8. Hausdorff spaces
  • 9. Connected spaces
  • 10. The pancake problems
  • 11. Manifolds and surfaces
  • 12. Paths and path connected spaces
  • 12A. The Jordan curve theorem
  • 13. Homotopy of continuous mappings
  • 14. 'Multiplication' of paths
  • 15. The fundamental group
  • 16. The fundamental group of a circle
  • 17. Covering spaces
  • 18. The fundamental group of a covering space
  • 19. The fundamental group of an orbit space
  • 20. The Borsuk-Ulam and ham-sandwhich theorems
  • 21. More on covering spaces: lifting theorems
  • 22. More on covering spaces: existence theorems
  • 23. The Seifert_Van Kampen theorem: I Generators
  • 24. The Seifert_Van Kampen theorem: II Relations
  • 25. The Seifert_Van Kampen theorem: III Calculations
  • 26. The fundamental group of a surface
  • 27. Knots: I Background and torus knots
  • 27. Knots : II Tame knots
  • 28A. Table of Knots
  • 29. Singular homology: an introduction
  • 30. Suggestions for further reading
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BA07660748
  • ISBN
    • 0521231957
    • 9780521298643
  • LCCN
    79041682
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge [Eng.] ; New York
  • ページ数/冊数
    viii, 269 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
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