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Introduction to Topology: Third Edition (Dover Books on Mathematics) Third Edition Edition

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ISBN-13: 978-0486663524
ISBN-10: 0486663523
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Editorial Reviews

From the Back Cover

Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.
The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology.
Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.
Unabridged Dover (1990) republication of the edition published by Allyn and Bacon, Inc., Boston 1975.

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 224 pages
  • Publisher: Dover Publications; Third Edition edition (July 1, 1990)
  • Language: English
  • ISBN-10: 0486663523
  • ISBN-13: 978-0486663524
  • Product Dimensions: 8.4 x 5.4 x 0.4 inches
  • Shipping Weight: 9.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (47 customer reviews)
  • Amazon Best Sellers Rank: #26,405 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

163 of 168 people found the following review helpful By Michael Wischmeyer on April 11, 2003
Format: Paperback
I was not a mathematics major, and only in recent years have I ventured into abstract mathematics. I was motivated to learn about topology as an aid to understanding a particular 3-D earth modeling application.

I read Introduction to Topology in three stages: as a review of set theory and metric spaces (chapters 1 and 2), then as an introduction to topology (chapter 3), and lastly as a detailed look at two important topological properties, connectedness (chapter 4) and compactness (chapter 5). I had previously read (and reviewed) another book titled Metric Spaces by Victor Bryant, but Mendelson is my first serious look at topology.

My reading of Mendelson - a 200-page text - required about 100 hours, substantially longer than the 40 to 60 hours estimated by an earlier reviewer. No solutions are provided for the section problems, which are generally proofs, not explicit problems.

The first chapter provides a concise overview of set theory and functions that is essential for Mendelson's later chapters on subsequent set-theoretic analysis of metric spaces and topology.

The second chapter is a solid introduction to metric spaces with good discussions on continuity, open balls and neighborhoods, limits from a metric space perspective, open sets and closed sets, subspaces, and equivalence of metric spaces. Chapter 2 concludes with a brief introduction to Hilbert space.

The third chapter introduces topological spaces as a generalization of metric spaces, and many theorems are largely restatements of the metric space theorems derived in chapter 2. I was thankful for this approach.
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66 of 70 people found the following review helpful By Marco Taboga mtaboga@tiscalinet.it on May 4, 2002
Format: Paperback
This book is ideal for self-study. If you have not had the luxury of taking a topology course during your undergraduate studies, but you need to know some topology and you have to study it by yourself, this is the book you need. It is very readable and it explains carefully every concept. However, it is just an introductory text and it contains only basic material. You don't have to invest a lot of time to study the material in this book: let's say 40-60 hours of study are enough to grasp everything. I reccomend it especially to those graduate students of applied mathematics, finance, statistics or economics, who need to use some basic result from topology in their work.
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32 of 33 people found the following review helpful By Brian Lauer on January 17, 2007
Format: Paperback
I bought this book for my own enlightenment after already having a course in Topology here at Penn State University. What I find most interesting about this book is that the author explains the philosophy on the ideas and what we are really trying to say with these definitions and theorems. The book I used in my course didn't explain much at all so it would have been much more difficult to teach yourself from this book. Topology is somewhat abstract so if you're looking to study Topology this is a great book to start. A word of advice, read over a theorem and proof and try to reproduce it on paper from your mind. Help yourself from the book a bit along the way if necessary. You will learn much more this way as opposed to following along the proofs in the book as you read. You might also be interested in Counterexamples in Topology, a book with thousands of counterexamples.
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15 of 15 people found the following review helpful By amr on June 30, 2009
Format: Paperback
I highly recommend this book. The problems are excellent. They really hit home and force you to truly understand the content. They get to the crux of the issues (some problems specifically test to make sure you didn't misinterpret a definition for example) and they're also interesting.

The book is carefully written in a simple style. It's a bit hard to explain... For lack of a better explanation, an analogy would be to how Mac computers are simple to use but not lacking in function. One specific example that I can pinpoint is that the author avoids using symbols excessively.

It is not a "layman" book at all however. Some problems take a lot of thinking. Some of them take me a few hours of scribbling in my notebooks and some of them take a few days of mulling over on top of that. But I'm not a math student or math practitioner (only a hobby at this point) so mathematicians-to-be should have an easier time than I.
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10 of 10 people found the following review helpful By Serious Inquirer on November 7, 2010
Format: Paperback Verified Purchase
Intended for the advanced undergraduate student with a respectable level of mathematical maturity, Mendelson begins with the necessary review of set theory. From there the book delves into metric spaces, topological spaces, connectedness, and compactness. In short, it presents the basics of topology in a clear, linear, very readable fashion.

Readers would be well advised to be familiar with the elements of proof, set theory, linear algebra, and abstract algebra in addition to analysis. A knowledge of geometry is also helpful, as one might expect.

Weighing the price of this book against the depth and breadth of other texts, this volume offers more to the student who is studying topology on a budget. Unfortunately, as with most books in this category, there is no solution guide provided for the exercises. A selection of hints for the exercises would have been a nice addition but otherwise does not detract from the purpose of the work: to give the beginning topologist an overview of the subject.
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