Customer Reviews:
Showing reviews 1-5 of 10
 Resource for deep knowledge of Point-Set Topology February 4, 2009
Biblio-luster
1 out of 1 found this review helpful
This book is a must have for anyone who wants to contribute to remaining questions in point-set topology. Property inheritance relationship diagrams fill the book, quickly giving someone a good knowledge of all the classic point-set properties of spaces more thoroughly than is ever taught in grad-school these days. The only draw back is that the book and counterexamples deal strictly with point-set. How nice it would be to have a new edition (or volume two) of this type of book pertaining to algebraic topology. For example, what is an example of a non-contractible space with all zero homotopy groups? This question (and any algebraic top. questions) wont be answered in Steen's book.
 Counterexamples in Topology March 27, 2007
Topology Student (New York)
1 out of 13 found this review helpful
I have found this book to be confusing to use and therefore of little to no value. If I had seen in a bookstore and not Online I would not have purchased it. I also purchased Schaum's Outline of General Topology which is very good.
 a veritable mine of information.... May 28, 2004
another reader (Victoria, Canada)
10 out of 10 found this review helpful
To paraphrase Chandrasekhar's review of Watson's Bessel functions text, this is "a veritable mine of information... indispensable to those who have occasion to use point-set topology." I don't think this book is intended to be a text (& I think the authors say so), in which case it would be terrible because it doesn't explain the concepts very much. It's mostly a catalogue of every kind of set you can come up with, every kind of topology you can put on it, and what properties it has such as what T_i axioms the space satisfies, whether it's compact, para compact, etc etc. Most of the time such things are proven, but be prepared to think hard sometimes about the proofs or fill in details. I'm the kind of student where I have trouble understanding things which are highly 'counter-intuitive' so I had trouble proving things, even when I knew definitions, when I did topology for the first time last term. Once I saw this book though I got used to all the weird things in topology (like the ordered square, R in the lower-limit topology, Sorgenfrey plane, etc etc). This book is incredibly useful as a reference.
Essential if you want to be good in point set topology February 26, 2004
bal gombak (Cambridge, MA USA)
24 out of 24 found this review helpful
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.
a good book to combine with a regular textbook December 3, 2002
Ruth Sprague (Seattle, WA USA)
32 out of 32 found this review helpful
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.
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