General Topology (Graduate Texts in Mathematics Series, Vol 27)

Rating:
Summary: May have been good in its day
Review: I cannot agree with the other reviewers on this. Back in the days when there were hardly any general texts on topology this may have been good. Nowadays there are at least a dozen such that are far better than this. The printing fonts and layout are spidery and primitive and not easy on the eye. The style is rather formal and dry for a subject as rich as this and little effort is put into illustrating the material with background, diagrams or examples. As I said before there is no shortage of better texts amongst which Hocking & Young is worth special mention.

Rating:
Summary: Topology with the analyst in mind!
Review: I don't hesitate to give this book 5 stars. It is solid! Many reviewers allow too much personal judgement to cloud their appraisal of a certain book. To me I believe it is important to be as dispassionate as possible so that a prospective buyer can make an unbiased decision. Rather than label a book as "bad" or "good" one should focus on some factors such as:
(1) Content: a summary of the main point covered by the book (this is optional). In the case of this book, this is obvious from the title.
(2) the author's approach: Kelly took what I call the "analyst's approach" to topology. This is fine for those who love analysis but don't really care for topology for it's own sake (like me!) By using this approach, those like me are much more inclined to find topology motivating because ones sees it as abstractions of what one is familiar with
(3) the presentation: Kelly gave a simple but "sophisticated" presentation. You will not describe him as very expository but the presentation is excellent. Some people seem to prefer this style and some don't. No, this has nothing to do with the so-called "mathematical maturity" (how do you define that by the way?) What the author expects you to know to understand the book - that is, the intended audience - is usually stated clearly in the preface

Rating:
Summary: The great classic of point set topology
Review: 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.

Rating:
Summary: best book I have read in every science
Review: the strength of the book is that you can have no background whatsoever in Topology (or even advanced calculus) and still be able to read it;
for me, the best book I have read in every science.
the reader will have to be at a certain level before attempting
to read it.

Rating:
Summary: Generally great; a few annoyances
Review: 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.