General Topology (Graduate Texts in Mathematics) [Hardcover]

John L. Kelley (Author)

Book Description

ISBN-10: 0387901256 | ISBN-13: 978-0387901251 | Publication Date: June 27, 1975

Aimed at graduate math students, this classic work is a systematic exposition of general topology and is intended to be a reference and a text. As a reference, it offers a reasonably complete coverage of the area, resulting in a more extended treatment than normally given in a course. As a text, the exposition in the earlier chapters proceeds at a pedestrian pace. A preliminary chapter covers those topics requisite to the main body of work.

Editorial Reviews

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. --This text refers to the Paperback edition.

Product Details

• Hardcover: 316 pages
• Publisher: Springer (June 27, 1975)
• Language: English
• ISBN-10: 0387901256
• ISBN-13: 978-0387901251
• Product Dimensions: 9.3 x 6.5 x 0.6 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #831,724 in Books (See Top 100 in Books)

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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, May 23, 2000

By 

henrique fleming - See all my reviews

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, November 5, 2005

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, January 2, 2005

By 

D. Feuer (Maryland, USA) - See all my reviews
(REAL NAME)   

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.