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General Topology, by John Leroy Kelley
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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.
- Sales Rank: #1071514 in Books
- Brand: Brand: Ishi Press
- Published on: 2008-09-10
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .71" w x 6.00" l, 1.02 pounds
- Binding: Paperback
- 314 pages
- Used Book in Good Condition
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.
Most helpful customer reviews
0 of 0 people found the following review helpful.
I don't think this would be a good text to learn from but I like to read ...
By Brian Paden
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.
0 of 1 people found the following review helpful.
Point Set Bible
By categorify
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.
14 of 14 people found the following review helpful.
excellent, but mainly a book of basic definitions and general concepts
By mathwonk
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".
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