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

Description

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.

User’s Reviews

Editorial Reviews: About the Author

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent reference

⭐Fast delivery, great condition of a book, nice package- highly recommend

⭐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.

⭐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.

⭐It’s very good.

⭐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”.

⭐This isn’t a bad book, but for any audience I can think of there is a better book to use than this one. If you are learning point set topology, use Munkres’ Topology, which is one of the most perfectly written books in mathematics. If you want to tighten your understanding of point set topology or to see more complicated examples than those in Munkres, use Counterexamples in Topology. If you are a working analyst who needs results in point set topology, like the fact that a product of at most continuum many separable Hausdorff spaces is separable, try Willard’s General Topology. An analyst may also need results on topological vector spaces, for which I recommend the first chapter of Rudin’s Functional Analysis and for more specialized results Treves’ Topological Vector Spaces. Kelley is certainly an historically important book, but I don’t see any reasons for someone learning topology now or doing work in analysis to use it any more. I strongly discourage an undergraduate learning point set topology to use this book as anything more than as a supplement to Munkres.

⭐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.

⭐Un gran libro que vale la pena tener en una biblioteca de matemáticasLivro excelente, muito bem escrito. É preciso se esforçar para alcançar o nível do livro, mas isso é bom.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.

⭐

Keywords

Free Download General Topology (Graduate Texts in Mathematics, 27) in PDF format
General Topology (Graduate Texts in Mathematics, 27) PDF Free Download
Download General Topology (Graduate Texts in Mathematics, 27) 1975 PDF Free
General Topology (Graduate Texts in Mathematics, 27) 1975 PDF Free Download
Download General Topology (Graduate Texts in Mathematics, 27) PDF
Free Download Ebook General Topology (Graduate Texts in Mathematics, 27)