Sinossi
Excellent text offers comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. The text is accessible to students at the advanced undergraduate or graduate level who are conversant with the basics of real analysis or advanced calculus. Problems, with selected solutions. Bibliography. 1975 edition.
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Contenuti
Preface "Chapter 1. Logic, Set Theory, and the Axiom of Choice" "This review chapter surveys elementary logic and set theory, including such concepts as countability, power set, etc. The axiom of choice is presented, along with its most useful variants. The chapter closes with an outline of category theory." Chapter 2. Metric Spaces "After a review of the real numbers, Euclidean spaces are studied in detail. This is followed by a treatment of all the basic properties of metric spaces and continuous functions from a metric space to another." Chapter 3. General Topological Spaces. Bases. Continuous Functions. Product Spaces ############################################################################################################################################################################################################################################################### Chapter 4. The Special Notions of Compactness and Connectedness ############################################################################################################################################################################################################################################################### "Chapter 5. Sequences, Countability, Separability, and Metrization" ############################################################################################################################################################################################################################################################### "Chapter 6. Quotients, Local Compactness, Tietze Extension, Complete Metrics, Baire Category" ############################################################################################################################################################################################################################################################### Chapter 7. Generalities about Manifolds; The Classification of Surfaces ############################################################################################################################################################################################################################################################### Chapter 8. The Fundamental Group "This is the first time where an algebraic invariant is introduced to study topological problems. The construction and basic properties occupy most of the chapter. At the end, the fundamental group is studied for Cartesian products and topological groups." Chapter 9. Covering Spaces ############################################################################################################################################################################################################################################################### Chapter 10. Calculation of Some Fundamental Groups. Applications ############################################################################################################################################################################################################################################################### Epilogue Bibliography Index of the Most Common Symbols Solutions to Selected Problems Index
Product Description
217p + publisher's catalogue, paperback with green cover, hardly used, edges a little yellowed but pages clean and unmarked, very good
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Topology: An Introduction to the Point-Set and Algebraic Areas (Dover Books on Mathematics)
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Dover Publications, 1995
ISBN 10: 0486686094
ISBN 13: 9780486686097
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Topology: An Introduction to the Point-Set and Algebraic Areas
Editore:
Dover Publications, 1995
ISBN 10: 0486686094
ISBN 13: 9780486686097
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Paperback. Condizione: Fair. No Jacket. Readable copy. Pages may have considerable notes/highlighting. ~ ThriftBooks: Read More, Spend Less. Codice articolo G0486686094I5N00
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Topology : An Introduction to the Point-Set and Algebraic Areas
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ISBN 10: 0486686094
ISBN 13: 9780486686097
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Topology: An Introduction to the Point-Set and Algebraic Areas (Dover Books on Mathematics)
Editore:
Dover Publications, 1995
ISBN 10: 0486686094
ISBN 13: 9780486686097
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Topology An Introduction to the Point-Set and Algebraic Areas
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Dover Publications, Incorporated, 1995
ISBN 10: 0486686094
ISBN 13: 9780486686097
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Topology: An Introduction to the Point-set and Algebraic Areas (Dover Books on Mathematics)
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Dover Publications Inc., 1995
ISBN 10: 0486686094
ISBN 13: 9780486686097
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