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  • Textbook
  • © 1993

Topology of Surfaces

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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eBook USD 54.99
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  • ISBN: 978-1-4612-0899-0
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Softcover Book USD 74.95
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
  2. Introduction to topology

    • L. Christine Kinsey
    Pages 1-6
  3. Point-set topology in ℝ n

    • L. Christine Kinsey
    Pages 7-36
  4. Point-set topology

    • L. Christine Kinsey
    Pages 37-55
  5. Surfaces

    • L. Christine Kinsey
    Pages 56-93
  6. The euler characteristic

    • L. Christine Kinsey
    Pages 94-124
  7. Homology

    • L. Christine Kinsey
    Pages 125-156
  8. Cellular functions

    • L. Christine Kinsey
    Pages 157-182
  9. Invariance of homology

    • L. Christine Kinsey
    Pages 183-196
  10. Homotopy

    • L. Christine Kinsey
    Pages 197-211
  11. Miscellany

    • L. Christine Kinsey
    Pages 212-234
  12. Topology and calculus

    • L. Christine Kinsey
    Pages 235-262
  13. Back Matter

    Pages 263-281

About this book

" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet­ describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu­ dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in­ tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.

Keywords

  • Separation axiom
  • compactness
  • topological invariant
  • topology

Authors and Affiliations

  • Department of Mathematics, Canisius College, Buffalo, USA

    L. Christine Kinsey

Bibliographic Information

  • Book Title: Topology of Surfaces

  • Authors: L. Christine Kinsey

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0899-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1993

  • Hardcover ISBN: 978-0-387-94102-8

  • Softcover ISBN: 978-1-4612-6939-7

  • eBook ISBN: 978-1-4612-0899-0

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: X, 281

  • Topics: Topology

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-0899-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 74.95
Price excludes VAT (USA)
Hardcover Book USD 74.95
Price excludes VAT (USA)