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A First Course in Topology: Continuity and Dimension
John McCleary, Vassar College, Poughkeepsie, NY
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Student Mathematical Library
2006; 210 pp; softcover
Volume: 31
ISBN-10: 0-8218-3884-9
ISBN-13: 978-0-8218-3884-6
List Price: US$38 Institutional Members: US$30.40
All Individuals: US\$30.40
Order Code: STML/31

Beginning Topology - Sue E Goodman

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Computational Topology: An Introduction - Herbert Edelsbrunner and John L Harer

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.

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..."