**Student Mathematical Library**

Volume: 31;
2006;
210 pp;
Softcover

MSC: Primary 54; 55;

Print ISBN: 978-0-8218-3884-6

Product Code: STML/31

List Price: $38.00

Individual Price: $30.40

**Electronic ISBN: 978-1-4704-2142-7
Product Code: STML/31.E**

List Price: $38.00

Individual Price: $30.40

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#### Supplemental Materials

# A First Course in Topology: Continuity and Dimension

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*John McCleary*

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincaré argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century.

The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time. The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension.

This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

#### Table of Contents

# Table of Contents

## A First Course in Topology: Continuity and Dimension

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Introduction vii8 free
- Chapter 1. A Little Set Theory 114 free
- Chapter 2. Metric and Topological Spaces 1528
- Chapter 3. Geometric Notions 2942
- Chapter 4. Building New Spaces from Old 4558
- Chapter 5. Connectedness 6780
- Chapter 6. Compactness 8396
- Chapter 7. Homotopy and the Fundamental Group 95108
- Chapter 8. Computations and Covering Spaces 111124
- Chapter 9. The Jordan Curve Theorem 129142
- Chapter 10. Simplicial Complexes 151164
- Chapter 11. Homology 171184
- Bibliography 201214
- Notation Index 207220
- Subject Index 209222
- Back Cover Back Cover1226

#### Readership

Undergraduate and graduate students interested in topology.

#### Reviews

It is rare to find a math book that is both succinct and thorough ... manages to present the central ideas of topology in a book that can be comfortably read within one or two weeks.

-- Math Horizons

McCleary offers a tight, purpose-built book, establishing the invariance of dimension, the rigorous structural distinction that differentiates lines from planes from higher-dimensional spaces.

-- CHOICE Magazine

This is a beautiful little book that may well become a classic packed with fascinating material students who work through it will learn a great deal, and emerge from the process much better mathematicians than they were before they began. It deserves many such readers.

-- MAA Reviews

This is a very nicely written elementary book on topology...

-- EMS Newsletter