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A First Course in Topology: Continuity and Dimension

John McCleary Vassar College, Poughkeepsie, NY
Available Formats:
Softcover ISBN: 978-0-8218-3884-6
Product Code: STML/31
210 pp
List Price: $41.00 Individual Price:$32.80
Electronic ISBN: 978-1-4704-2142-7
Product Code: STML/31.E
210 pp
List Price: $38.00 Individual Price:$30.40
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List Price: $61.50 Click above image for expanded view A First Course in Topology: Continuity and Dimension John McCleary Vassar College, Poughkeepsie, NY Available Formats:  Softcover ISBN: 978-0-8218-3884-6 Product Code: STML/31 210 pp  List Price:$41.00 Individual Price: $32.80  Electronic ISBN: 978-1-4704-2142-7 Product Code: STML/31.E 210 pp  List Price:$38.00 Individual Price: $30.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$61.50
• Book Details

Student Mathematical Library
Volume: 312006
MSC: Primary 54; 55;

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.

• Chapters
• Chapter 1. A little set theory
• Chapter 2. Metric and topological spaces
• Chapter 3. Geometric notions
• Chapter 4. Building new spaces from old
• Chapter 5. Connectedness
• Chapter 6. Compactness
• Chapter 7. Homotopy and the fundamental group
• Chapter 8. Computations and covering spaces
• Chapter 9. The Jordan Curve Theorem
• Chapter 10. Simplicial complexes
• Chapter 11. Homology

• 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...

• Request Review Copy
• Get Permissions
Volume: 312006
MSC: Primary 54; 55;

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.

• Chapters
• Chapter 1. A little set theory
• Chapter 2. Metric and topological spaces
• Chapter 3. Geometric notions
• Chapter 4. Building new spaces from old
• Chapter 5. Connectedness
• Chapter 6. Compactness
• Chapter 7. Homotopy and the fundamental group
• Chapter 8. Computations and covering spaces
• Chapter 9. The Jordan Curve Theorem
• Chapter 10. Simplicial complexes
• Chapter 11. Homology
• 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...