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A Taste of Topology

  • Volker Runde
  • S Axler
  • K.A. Ribet

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Pages 1-3
  3. Pages 5-22
  4. Pages 23-60
  5. Pages 61-108
  6. Pages 133-167
  7. Back Matter
    Pages 169-176

About this book

Introduction

If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language.

The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set-theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students can benefit from some parts.

Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis.

In some points, the book treats its material differently than other texts on the subject:

* Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem;

* Nets are used extensively, in particular for an intuitive proof of  Tychonoff's theorem;

* A short and elegant, but little known proof for the Stone-Weierstrass theorem is given.

Keywords

Algebraic topology set topology

Authors and affiliations

  • Volker Runde
    • 1
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

Editors and affiliations

  • S Axler
    • 1
  • K.A. Ribet
    • 2
  1. 1.Mathematics DepartmentSan Francisco State UniversitySan FranciscoUSA
  2. 2.Mathematics DepartmentUniversity of California at BerkeleyBerkeleyCAUSA

Bibliographic information