- Paperback: 314 pages
- Publisher: Ishi Press (10 Sep 2008)
- Language English
- ISBN-10: 0923891552
- ISBN-13: 978-0923891558
- Product Dimensions: 2.3 x 1.5 x 0.2 cm
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
- Amazon Bestsellers Rank: 920,162 in Books (See Top 100 in Books)
General Topology (Graduate Texts in Mathematics)
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Product Description
Product Description
General Topology is not only a textbook, it is also an invaluable reference work for all mathematicians working the field of analysis. It has long been out of print, but a whole generation of mathematicians, including myself, learned their topology from this book. There are no wasted words in Kelley's presentation; every sentence is short and to the point, but the student would do well to contemplate each of them, for they are pregnant with subtle implications. The numerous problems that follow each chapter are well chosen to complete the students' understanding of the topics discussed. THIS VOLUME gives a systematic exposition of the part of general topology which has proven useful in several branches of mathematics and is intended especially as a background for modern analysis. One of the many features of this volume is the wealth and diversity of problem material which includes counter-examples and numerous applications of general topology to different fields. The appendix, which is entirely independent of the rest of the book, includes an axiomatic treatment of set theory. The author has included the most commonly used terminology, and all terms are listed in the index. As a reference, this book offers a unique coverage of topology with recent contributions to the field.
About the Author
JOHN L. KELLEY, was the national teacher for the Continental Classroom modern algebra course and Professor of Mathematics and Chairman of the Department of Mathematics at the University of California at Berkeley. Before joining the Berkeley faculty in 1947, he taught at the Universities of Notre Dame and Chicago. He served as visiting associate professor at Tulane University and the University of Kansas and as Fulbright Research Professor at Cambridge University. Dr. Kelley was a Fellow at the Institute for Advanced Study, Princeton, N. J., in 1945-46 and a National Science Foundation Post Doctoral Fellow in 1953-54. His other publications include Introduction to Modern Algebra (1960) and Exterior Ballistics (with Edward James McShane and F. V. Reno, 1953) as well as numerous research papers dealing with general topology and functional analysis. Dr. Kelley, was a member of the American Mathematical Society, the Committee on the Undergraduate Program of the Mathematical Association of America, and the Panel on Teacher Training of the School Mathematics Study Group.
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Customer Reviews
Most Helpful Customer Reviews
6 of 6 people found the following review helpful
Format:Hardcover
The title of my review might be surprising, since this is supposed to be a book on topology. But Kelley says it best in his introduction: he intended to subtitle his book "What Every Young Analyst Should Know." As such, you will only find point set topology in this book--no algebraic or differential topology, and no mention of manifolds. I suppose the point of the book is to shed light on the topological structure of spaces of continuous functions on locally compact, Hausdorff spaces. This is really too restrictive to do the book justice, though. Kelley also discusses nets (vital in functional analysis, where non-metrisable topologies abound), characterisation of metrisability, uniform spaces, etc. Anyone interested in analysis, particularly functional analysis, should be familiar with these topics, since function spaces often have topologies which are not metrisable. In such spaces, sequences are often not enough to test for closure--nets must be used. Similarly, uniform and Cauchy properties must be reformulated in the guise of uniformities. Kelley leads the reader through all of these thickets in a clear style.
The only complaint that can be made against Kelley's book is the lack of examples in text. However, he makes up for this with numerous exercises that generally revolve around important examples of topics discussed in that chapter. Despite his lack of examples, the text is still quite clear. His proofs are very complete, and he is a true stickler for detail, something that is vital in such an abstract setting as general topology. To wrap up this review, if you are interested in "topology" as usually considered at universities, this probably is not the book for you--it is an excellent reference for point set topology, but the powerful machinery of algebraic and differential topology is not here.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
6 reviews
33 of 36 people found the following review helpful
The great classic of point set topology
24 May 2000
Format: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.
19 of 22 people found the following review helpful
a splendid technical book
6 Nov 2005
Format: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.
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 16 people found the following review helpful
Generally great; a few annoyances
3 Jan 2005
Format: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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