Elementary Topology [Paperback]

Dennis Roseman (Author)

Book Description

Publication Date: June 20, 1999 | ISBN-10: 0138638799 | ISBN-13: 978-0138638795 | Edition: 1

This book offers a thorough introduction to the important topics of topology, a variety of interesting, concrete examples, and ample opportunity and guidance for building reasoning skills and writing proofs. It uses a unique, less-abstract, more example-driven approach that uses the setting of Euclidean space — mostly the line, the plane and 3-dimensional space. Focuses on Rn. Covers: Open and Closed Subsets; Building Open and Closed Subsets; Continuity; Homeomorphism; Cantor Sets and Similar Constructions; Embeddings; Connectivity; Path Connectedness; Closure, Limit Points, and Limit Points of Sequences; Compactness; Local Connectivity; Space Filling Curves; Manifolds; Simple Connectivity; Deformation Type; Knots and Knottings; Complexes; Higher Dimensions; and The Poincare “Conjecture.” For anyone who needs an introduction to topology.

Editorial Reviews

From the Back Cover

This book offers a thorough introduction to the important topics of topology, a variety of interesting, concrete examples, and ample opportunity and guidance for building reasoning skills and writing proofs. It uses a unique, less-abstract, more example-driven approach that uses the setting of Euclidean space — mostly the line, the plane and 3-dimensional space. Focuses on Rn. Covers: Open and Closed Subsets; Building Open and Closed Subsets; Continuity; Homeomorphism; Cantor Sets and Similar Constructions; Embeddings; Connectivity; Path Connectedness; Closure, Limit Points, and Limit Points of Sequences; Compactness; Local Connectivity; Space Filling Curves; Manifolds; Simple Connectivity; Deformation Type; Knots and Knottings; Complexes; Higher Dimensions; and The Poincare “Conjecture.” For anyone who needs an introduction to topology.

Product Details

• Paperback: 448 pages
• Publisher: Prentice Hall; 1 edition (June 20, 1999)
• Language: English
• ISBN-10: 0138638799
• ISBN-13: 978-0138638795
• Product Dimensions: 9.3 x 6.3 x 0.9 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 2.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #2,589,767 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

2.0 out of 5 stars I don't like this book, November 15, 2002

By 

Zachary Turner (San Francisco, CA) - See all my reviews

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This review is from: Elementary Topology (Paperback)

We used this book for the first undergraduate topology course at my university. Perhaps the book is okay if you know what to expect from it before you buy it. What this book IS NOT is a book on General Topology. What this book IS is a book on the topology of the real number system. It's odd, because the course I took is one on general topology, where the topology of the real number system was mentioned as a mere footnote, yet this book covers very little general topology. At the end of each chapter, there is a starred section, in which about 1 page is devoted to how these concepts apply to general topology. So if that's what you want, perhaps you'll like this book. But that's not the only reason I didn't like it.

This book states EVERYTHING as a proposition. It gets ridiculous, there's so many propositions. In one section of one chapter I counted almost 40 propositions once. Unbelievable. Many results are not proved, which leaves alot to be desired in that department, and alot of the exercises are "give an example of...". These types of problems are great, but all in all there just isn't enough variety in this book for me.

So, if you're looking for a book on General Topology this definitely is not the one you want. If you're looking for a book on Topology of Rn, then I'd say you can consider this book rated 3.5 stars, and you can make your decision based on that.

However, if that's really all you want, you can find the same results in any modern analysis book such as Baby Rudin (i.e. Principles of Mathematical Analysis), and for general topology the book(s) to go to are Munkres' Topology, and Kelley's General Topology.

2.0 out of 5 stars Not a Very Good Book, January 15, 2006

By 

Markh (Ames, IA) - See all my reviews

This review is from: Elementary Topology (Paperback)

I can't recommend this book. It seemed sloppily written and edited, with numerous errors. The fact that the author largely limits himself to Euclidean spaces may or may not, depending on your needs, be a big drawback, but the carelessness of the writing really detracts from its usefulness.

0 of 1 people found the following review helpful:

2.0 out of 5 stars Not Great For Point-Set Topology, May 16, 2008

By 

Patrick Thompson "Patrick" (Nassau, Bahamas) - See all my reviews

Amazon Verified Purchase

This review is from: Elementary Topology (Paperback)

This book was required for the class I did in undergraduate topology. I didn't like this book at all. I can not highly recommend it's use as a class text, perhaps as a reference book. There are much better books on general topology out there.