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A Guide to Topology

A Guide to Topology


Part of Dolciani Mathematical Expositions

  • Date Published: September 2009
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Hardback
  • isbn: 9780883853467

£ 35.99

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About the Authors
  • A Guide to Topology is an introduction to basic topology for graduate or advanced undergraduate students. It covers point-set topology, Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations. Students studying for exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too.

    • A short, sharp introduction that shows readers exactly what topology is and why it is useful
    • Concludes with function spaces to acquaint students with the applications of the basic ideas and techniques of topology
    • Includes table of notation and glossary to help students get to grip with the material quickly
    Read more

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    Product details

    • Date Published: September 2009
    • format: Hardback
    • isbn: 9780883853467
    • length: 120 pages
    • dimensions: 235 x 157 x 11 mm
    • weight: 0.28kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    Part I. Fundamentals:
    1.1. What is topology?
    1.2. First definitions
    1.3 Mappings
    1.4. The separation axioms
    1.5. Compactness
    1.6. Homeomorphisms
    1.7. Connectedness
    1.8. Path-connectedness
    1.9. Continua
    1.10. Totally disconnected spaces
    1.11. The Cantor set
    1.12. Metric spaces
    1.13. Metrizability
    1.14. Baire's theorem
    1.15. Lebesgue's lemma and Lebesgue numbers
    Part II. Advanced Properties:
    2.1 Basis and subbasis
    2.2. Product spaces
    2.3. Relative topology
    2.4. First countable and second countable
    2.5. Compactifications
    2.6. Quotient topologies
    2.7. Uniformities
    2.8. Morse theory
    2.9. Proper mappings
    2.10. Paracompactness
    Part III. Moore-Smith Convergence and Nets:
    3.1. Introductory remarks
    3.2. Nets
    Part IV. Function Spaces:
    4.1. Preliminary ideas
    4.2. The topology of pointwise convergence
    4.3. The compact-open topology
    4.4. Uniform convergence
    4.5. Equicontinuity and the Ascoli-Arzela theorem
    4.6. The Weierstrass approximation theorem
    Table of notation

  • Author

    Steven G. Krantz, Washington University, St Louis
    Steven G. Krantz was born in San Francisco, California and grew up in Redwood City, California. He received his undergraduate degree from the University of California at Santa Cruz and the Ph.D. from Princeton University. Krantz has held faculty positions at UCLA, Princeton University, Penn State University, and Washington University in St. Louis. He is currently Deputy Director of the American Institute of Mathematics. He has written 160 scholarly papers, over 50 books and is the holder of the Chauvenet Prize and the Beckenbach Book Award.

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