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John L. Kelley
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General Topology (Graduate Texts in Mathematics, 27)

by John L. Kelley (Author)
4.7 4.7 out of 5 stars 42 ratings
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This classic book is a systematic exposition of general topology. It is especially intended as background for modern analysis. Based on lectures given at the University of Chicago, the University of California and Tulane University, this book is intended to be a reference and a text. As a reference work, it offers a reasonably complete coverage of the area, and this has resulted in a more extended treatment than would normally be given in a course. As a text, however, the exposition in the eariler chapters proceeds at a more pedestrian pace. A preliminary chapter covers those topics requisite to the main body of work.
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  1. ISBN-10
    0387901256
  2. ISBN-13
    978-0387901251
  3. Publisher
    Springer
  4. Publication date
    June 27, 1975
  5. Language
    English
  6. Dimensions
    6.24 x 0.76 x 9.49 inches
  7. Print length
    312 pages
  8. See all details
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Product details

  • Publisher ‏ : ‎ Springer (June 27, 1975)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 312 pages
  • ISBN-10 ‏ : ‎ 0387901256
  • ISBN-13 ‏ : ‎ 978-0387901251
  • Item Weight ‏ : ‎ 3.02 pounds
  • Dimensions ‏ : ‎ 6.24 x 0.76 x 9.49 inches
  • Customer Reviews:
    4.7 4.7 out of 5 stars 42 ratings

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  1. John L. Kelley

    John L. Kelley

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  2. C. C. Marouchos

    C. C. Marouchos

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Customer reviews

4.7 out of 5 stars
4.7 out of 5
42 global ratings

Top reviews from the United States

Vicki Wright
5.0 out of 5 stars A Classic
Reviewed in the United States on November 22, 2022
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Excellent reference
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Leo
5.0 out of 5 stars Fast delivery, great condition
Reviewed in the United States on August 28, 2021
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Fast delivery, great condition of a book, nice package- highly recommend
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BP1988
5.0 out of 5 stars I don't think this would be a good text to learn from but I like to read ...
Reviewed in the United States on October 29, 2016
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I don't think this would be a good text to learn from but I like to read old ones to see how the language and notation has changed over time.
5 people found this helpful
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some none else
5.0 out of 5 stars Point Set Bible
Reviewed in the United States on December 19, 2013
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Literally contains everything in point set topology that a young mathematician could need - from basic axioms to advanced topics like uniform spaces. The heart of this book, however, is its collection of challenging and instructive exercises.
5 people found this helpful
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KI
5.0 out of 5 stars Five Stars
Reviewed in the United States on May 2, 2017
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It's very good.
One person found this helpful
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mathwonk
5.0 out of 5 stars excellent, but mainly a book of basic definitions and general concepts
Reviewed in the United States on March 18, 2013
After senior year in college I read through most of this book and learned once and for all the basic facts of life about open and closed sets, continuity, product and quotient spaces, compactifications, nets, filters, and uniform spaces. Then for the rest of my life as a budding differential topologist, several complex variables analyst, and finally algebraic geometer, I never looked at it again, and never used the concept of a net or uniform space again either. Moreover when I began to take topology courses from topologists instead of analysts, I realized I understood essentially nothing about topology, since I had learned nothing here about the most fundamental examples such as spheres, lens spaces, tori, manifolds, etc..., not to mention homotopy, Eilenberg Maclane spaces, Postnikov towers,.... One can read this whole book and do all the exercises and still not know whether different dimensional spheres are homeomorphic. To me the really interesting topology is algebraic and differential topology and this is not even hinted at here.

This book is very formal and not at all intuitive. As a young man, thinking math is a formal game, I enjoyed this, as it seemed divorced from other subjects and stood beautifully alone. You could just memorize all the definitions and get a perfect score on a test. But eventually one wants to be able to see how various subjects are related to each other. This book does an excellent job of teaching the fundamental language of convergence, but very little else. This material is basic to many mathematical subjects but does not go far into any of them. I recommend it as a start, but warn the reader that he still knows very little afterwards other than language, and a few density and compactification theorems. Many of us really will not use Stone Cech compactifications very much, interesting as they are abstractly. One more plus for the book, his treatment of set theory in an appendix is very nice, and frequently cited. I give it 5 stars for what it is, a fine textbook of basic general topology, but want to apprise you of what the limitations are. It is appropriately titled, but if you are a novice as I was, try not to confuse "general topology" with topology. I regard this as analogous to an excellent grammar book, but one needs to read some literature eventually. This is mostly the sort of basic material that is either assumed or taught in the first semester of grad school in math. For me, it might actually have been helpful if it had been titled "what every young analyst should know".
38 people found this helpful
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Amazon Customer
5.0 out of 5 stars a splendid technical book
Reviewed in the United States on November 6, 2005
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.
24 people found this helpful
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henrique fleming
5.0 out of 5 stars The great classic of point set topology
Reviewed in the United States on May 24, 2000
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.
44 people found this helpful
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Mr John Graham
1.0 out of 5 stars Don't buy this in hardback
Reviewed in the United Kingdom on August 11, 2023
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I have no problems with the contents of the book : Kelley's book is very , very good . However, this hardback edition from Hassell Street Press is a disgrace . The overall quality of this hardback leads me to the opinion that it's best not to use it to read this very good work but to put it in the toilet , tear out the pages and wipe your arse on them as and when the need arises. Hassell - should that be Hassle - have just taken a very poorly looked-after library copy of this books ( there are lots of underscoring and writing in margins etc ) and made a very bad photo copy of the whole book . The whole production smacks of something someone has produced in their back bedroom . To sum up , get the Dover paperback . Avoid,avoid this hardback
One person found this helpful
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Francisco
5.0 out of 5 stars Es un clásico imprescindible
Reviewed in Spain on July 13, 2022
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Un gran libro que vale la pena tener en una biblioteca de matemáticas
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Marcelo Barboza
5.0 out of 5 stars Muito bom livro.
Reviewed in Brazil on April 3, 2020
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Livro excelente, muito bem escrito. É preciso se esforçar para alcançar o nível do livro, mas isso é bom.
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David
5.0 out of 5 stars Excelente.
Reviewed in Spain on July 27, 2014
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Es un excelente libro, con una teoría bien fundamentada, y una serie de ejercicios bastante retadores. Muy recomendado para quien quiera iniciarse en la topología.
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