Counterexamples in Topology (Dover Books on Mathematics) [Paperback]

Lynn Arthur Steen (Author), J. Arthur Seebach Jr. (Author)

Book Description

ISBN-10: 048668735X | ISBN-13: 978-0486687353 | Publication Date: September 22, 1995

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.

Product Details

• Paperback: 272 pages
• Publisher: Dover Publications (September 22, 1995)
• Language: English
• ISBN-10: 048668735X
• ISBN-13: 978-0486687353
• Product Dimensions: 8.4 x 5.4 x 0.5 inches
• Shipping Weight: 9.1 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #229,371 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

39 of 39 people found the following review helpful:

4.0 out of 5 stars a good book to combine with a regular textbook, December 3, 2002

By 

Ruth Sprague (Seattle, WA USA) - See all my reviews
(REAL NAME)   

This review is from: Counterexamples in Topology (Dover Books on Mathematics) (Paperback)

This book has examples in it that are "missing", so to speak, from many regular topology books. It aims to shore up some of these shortcomings, with examples that the student can see and understand. There are charts and graphs, as well as a detailed explanation. Some "problems" often found in regular topology books are solved. Very few proofs, if any, are given. This is not a book meant to be studied without a regular textbook on topology, only to be used as an overall review of problems and short basic premises of topology. Use this in addition to your regular fare, but keep it close at hand when doing homework or preparing for an exam.
There are fundamentals on Cantor's Theorem, the countability or uncountability of sets, compactness, closed and bounded functions, open sets, continuity, connectedness, etc. All these are basic to topology, and this book does address them, but in a brief way. It then shows a basic overview of topology that helps greatly to understand the different fields of topology.

38 of 38 people found the following review helpful:

5.0 out of 5 stars Essential if you want to be good in point set topology, February 25, 2004

By 

bal gombak (Cambridge, MA USA) - See all my reviews

This review is from: Counterexamples in Topology (Dover Books on Mathematics) (Paperback)

A distinct characteristic of point set topology is that it builds on counterexamples. If you thumb through any PST text, many theorems are in the form "If the space T is A,B,C, then the space is X,Y,Z". The point of point set topology (pun unintended) is too determine what A,B,C are, and to weaken the hypothesis. "Can we take condition B out? Maybe hypothesis C can be weaken considerably?" How can we answer these questions? You're right, by counterexamples. Students who want to master point set topology should know the various counterexamples, no matter how contrived or unnatural they seem. While textbooks usually present a counterexample to show why Theorem Three Point Five Oh will not work on a weaker assumption -- most students (and teachers) tend to skip these parts. A collection of counterexamples presented in this book (excellent organisation, by the way) is an essential supplement of a topology course; it enables one to 'see' between the points, so to speak.

26 of 26 people found the following review helpful:

5.0 out of 5 stars Great Book, December 11, 2001

By 

Joseph Borrego (Leverett, MA United States) - See all my reviews

This review is from: Counterexamples in Topology (Dover Books on Mathematics) (Paperback)

As a graduate I encountered a book called "counter examples in analysis" which I found very useful. I always dreamed of such a book in topology, this book exceeds my dreams. It is great. It does not cover all the examples that I have used over the decades but it does cover some that I have never seen. The style is quite readable for a professional topologist. The book goes into a lot of interesting details (and some while not interesting to me would be another person). In short for me it is an essential book. The question is to whom else would this be interesting to. It is clearly of little use to a first year student and less to more advanced student. It's brand of topology is not the current cutting edge. So the audience for this book is limited to a small group and for these people it is top notch.