A First Course in Algebraic Topology

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9780521231954: A First Course in Algebraic Topology
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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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Descrizione del libro:

This self-contained introduction to algebraic topology is suitable for a number of topology courses. 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.

Contenuti:

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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9780521298643: A First Course in Algebraic Topology

Edizione in evidenza

ISBN 10: 0521298644 ISBN 13: 9780521298643
Casa editrice: Cambridge University Press, 2009
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Kosniowski, Czes
Editore: Cambridge University (1980)
ISBN 10: 0521231957 ISBN 13: 9780521231954
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Valutazione libreria

Descrizione libro Cambridge University, 1980. Condizione: Good. *Price HAS BEEN REDUCED by 10% until Monday, April 19 (sale item)* 269 pp., hardcover, ex library else text clean & binding tight in a worn dust jacket. Codice articolo ZB1194709

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