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Topological Spaces

From Distance to Neighborhood

  • Gerard Buskes
  • Arnoud van Rooij

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. The Line and the Plane

    1. Front Matter
      Pages 1-1
    2. Gerard Buskes, Arnoud van Rooij
      Pages 3-22
    3. Gerard Buskes, Arnoud van Rooij
      Pages 23-35
    4. Gerard Buskes, Arnoud van Rooij
      Pages 36-51
    5. Gerard Buskes, Arnoud van Rooij
      Pages 52-78
  3. Metric Spaces

    1. Front Matter
      Pages 79-79
    2. Gerard Buskes, Arnoud van Rooij
      Pages 81-98
    3. Gerard Buskes, Arnoud van Rooij
      Pages 99-116
    4. Gerard Buskes, Arnoud van Rooij
      Pages 117-128
    5. Gerard Buskes, Arnoud van Rooij
      Pages 129-143
    6. Gerard Buskes, Arnoud van Rooij
      Pages 144-155
    7. Gerard Buskes, Arnoud van Rooij
      Pages 156-170
    8. Gerard Buskes, Arnoud van Rooij
      Pages 171-184
  4. Topological Spaces

    1. Front Matter
      Pages 185-185
    2. Gerard Buskes, Arnoud van Rooij
      Pages 187-201
    3. Gerard Buskes, Arnoud van Rooij
      Pages 202-214
    4. Gerard Buskes, Arnoud van Rooij
      Pages 215-230
    5. Gerard Buskes, Arnoud van Rooij
      Pages 231-248
    6. Gerard Buskes, Arnoud van Rooij
      Pages 249-269
    7. Gerard Buskes, Arnoud van Rooij
      Pages 270-282
  5. Postscript

    1. Front Matter
      Pages 283-283
    2. Gerard Buskes, Arnoud van Rooij
      Pages 285-294
    3. Gerard Buskes, Arnoud van Rooij
      Pages 295-303
  6. Back Matter
    Pages 304-315

About this book

Introduction

This book is a text, not a reference, on Point-set Topology. It addresses itself to the student who is proficient in Calculus and has some experience with mathematical rigor, acquired, e.g., via a course in Advanced Calculus or Linear Algebra. To most beginners, Topology offers a double challenge. In addition to the strangeness of concepts and techniques presented by any new subject, there is an abrupt rise of the level of abstraction. It is a bad idea to teach a student two things at the same moment. To mitigate the culture shock, we move from the special to the general, dividing the book into three parts: 1. The Line and the Plane 2. Metric Spaces 3. Topological Spaces. In this way, the student has ample time to get acquainted with new ideas while still on familiar territory. Only after that, the transition to a more abstract point of view takes place. Elementary Topology preeminently is a subject with an extensive ar­ray of technical terms indicating properties of topological spaces. In the main body of the text, we have purposely restricted our mathematical vocabulary as much as is reasonably possible. Such an enterprise is risky. Doubtlessly, many readers will find us too thrifty. To meet them halfway, in Chapter 18 we briefly introduce and discuss a number of topological properties, but even there we do not touch on paracompactness, com­plete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric.

Keywords

Compact space Compactification Connected space Mathematica PostScript boundary element method compactness geometry knowledge learning meager set metrics set sets topology

Authors and affiliations

  • Gerard Buskes
    • 1
  • Arnoud van Rooij
    • 2
  1. 1.Department of MathematicsUniversity of Mississippi UniversityUSA
  2. 2.Department of MathematicsCatholic University of NijmegenNijmegenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0665-1
  • Copyright Information Springer-Verlag New York, Inc 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6862-8
  • Online ISBN 978-1-4612-0665-1
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site