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Topological Spaces

From Distance to Neighborhood

  • Textbook
  • © 1997

Overview

Authors:
  1. Gerard Buskes

    1. Department of Mathematics, University of Mississippi University, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Arnoud Rooij

    1. Department of Mathematics, Catholic University of Nijmegen, Nijmegen, The Netherlands

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xi
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  2. The Line and the Plane

    1. Front Matter

      Pages 1-1
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    2. What Topology Is About

      • Gerard Buskes, Arnoud van Rooij
      Pages 3-22

    3. Axioms for ℝ

      • Gerard Buskes, Arnoud van Rooij
      Pages 23-35

    4. Convergent Sequences and Continuity

      • Gerard Buskes, Arnoud van Rooij
      Pages 36-51

    5. Curves in the Plane

      • Gerard Buskes, Arnoud van Rooij
      Pages 52-78

  3. Metric Spaces

    1. Front Matter

      Pages 79-79
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    2. Metrics

      • Gerard Buskes, Arnoud van Rooij
      Pages 81-98

    3. Open and Closed Sets

      • Gerard Buskes, Arnoud van Rooij
      Pages 99-116

    4. Completeness

      • Gerard Buskes, Arnoud van Rooij
      Pages 117-128

    5. Uniform Convergence

      • Gerard Buskes, Arnoud van Rooij
      Pages 129-143

    6. Sequential Compactness

      • Gerard Buskes, Arnoud van Rooij
      Pages 144-155

    7. Convergent Nets

      • Gerard Buskes, Arnoud van Rooij
      Pages 156-170

    8. Transition to Topology

      • Gerard Buskes, Arnoud van Rooij
      Pages 171-184

  4. Topological Spaces

    1. Front Matter

      Pages 185-185
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    2. Topological Spaces

      • Gerard Buskes, Arnoud van Rooij
      Pages 187-201

    3. Compactness and the Hausdorff Property

      • Gerard Buskes, Arnoud van Rooij
      Pages 202-214

    4. Products and Quotients

      • Gerard Buskes, Arnoud van Rooij
      Pages 215-230

    5. The Hahn-Tietze-Tong-Urysohn Theorems

      • Gerard Buskes, Arnoud van Rooij
      Pages 231-248

    6. Connectedness

      • Gerard Buskes, Arnoud van Rooij
      Pages 249-269
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Mississippi University, USA

    Gerard Buskes

  • Department of Mathematics, Catholic University of Nijmegen, Nijmegen, The Netherlands

    Arnoud Rooij

Bibliographic Information

  • Book Title: Topological Spaces

  • Book Subtitle: From Distance to Neighborhood

  • Authors: Gerard Buskes, Arnoud Rooij

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0665-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-387-94994-9Published: 15 August 1997

  • Softcover ISBN: 978-1-4612-6862-8Published: 13 October 2012

  • eBook ISBN: 978-1-4612-0665-1Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XI, 313

  • Topics: Topology

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