A first course in algebraic topology

著者

• Kosniowski, Czes

書誌事項

A first course in algebraic topology

Czes Kosniowski

Cambridge University Press, 1980

• pbk.

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.

「Nielsen BookData」 より

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:
  • LCC : QA612
  • DC : 514/.2
• 件名:
  • LCSH : Algebraic topology