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Most Helpful Customer Reviews
32 of 35 people found the following review helpful:
5.0 out of 5 stars
The great classic of point set topology,
This review is from: General Topology (Graduate Texts in Mathematics) (Hardcover)
John Kelley wanted the title to be "What every young analyst should know", but was convinced (by Halmos, among others) not to use it. Still, it is a very good description of the book. Barry Simon calls it "superb" and recommends that you read it by trying to do the exercises, recurring to the text as needed. But then you would perhaps not pay attention to how wonderful the text is. I believe this is the best-written modern mathematical text. The proofs are clean and extremely elegant. The prose itself is beautiful and frequently witty. Treats topological and uniform spaces at depth and in detail, so as to be both a textbook and a reference. Excels in both capacities. This is mathematics close to poetry.
18 of 21 people found the following review helpful:
5.0 out of 5 stars
a splendid technical book,
By a reader (USA) - See all my reviews
This review is from: General Topology (Graduate Texts in Mathematics) (Hardcover)
I was motivated to read this book while in grad school, becasue I needed to understand the French literature in my field (probability). One particular concern is the metrizability of a general topological space. I would say Kelley's book has a spendid presentation on this subject.
Other things in this book are also practically useful. Convergence in the general sense (net or filter) is useful in mathematical finance. The part on locally compactness and paracompactness is a must for anyone working in differential geometry. And if you work in analysis, then the chapter on space of continuous functions is a good reference to look up. The exercise problems are also good resources when you need some help. I still remember one cute problem on the neighbourhood systems. It helped me understand how a family of seminorms would yield a topology on a linear space. Evetually, I read this book from cover to cover. And I would say this is one of the best education I've ever received. If there has to be a complain, the proofs are somewhat hard to read. But this is more or less determined by the nature of the subjects. And when you are well-motivated and equipped with certain mathematical maturity, this problem will gradually go off. In summary, this book is comprehensive, useful and beautifully written. It is a treasure that every mathematician's library should have.
11 of 15 people found the following review helpful:
4.0 out of 5 stars
Generally great; a few annoyances,
By
This review is from: General Topology (Graduate Texts in Mathematics) (Hardcover)
This is a great book. The proofs are clearly presented, and generally it is easy to understand the motivation behind definitions and theorems. Exercises are relevant, interesting, and well designed, often allowing the reader to discover things that other texts describe in dull detail. Unfortunately, a few exercises (such as "Integration Theory: Junior Grade") seem to pop out of nowhere. I consider this a minor defect. A much larger annoyance is that Kelley defines partial and linear orders in an utterly non-standard and somewhat clumsy way, which ends up affecting a large number of exercises. If you already know something about orderings, you will encounter many surprises; if you know nothing about them, you may get the wrong idea.
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