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A First Course in Algebraic Topology

  • Date Published: November 1980
  • availability: Available
  • format: Paperback
  • isbn: 9780521298643

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  • 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.

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    Product details

    • Date Published: November 1980
    • format: Paperback
    • isbn: 9780521298643
    • length: 280 pages
    • dimensions: 229 x 152 x 16 mm
    • weight: 0.41kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    Czes Kosniowski

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