Introduction to Topology: Third Edition (Dover Books on Mathematics)

Overall, great introductory book to topology. The pedagogy was excellent and the development of topics <i>made sense</i> in going from metric spaces (a notion that is general more intuitive) to abstract topological spaces. In particular, it was great for self-study as Mendelson doesn't shy away from fully fleshing-out proofs and repeating relatively similar cases with some additional notes (e.g. when going from metric to topological spaces and proving several ideas there). The book itself can certainly be read by anyone with a set theory background and some intuitive notion of limits/sequences (i.e. a class in pre-calculus), but that doesn't mean it's easy, <i>by any means</i>. I struggled quite a bit with the intuition behind some of the proofs, and have, more than once, rolled around on my bed trying to recall (or prove again) some particular statement that I found quite useful. Sadly, the book doesn't have a section on homotopy equivalence and some other useful notions, but do recall it is an introduction in exactly 200 pages of short text. This book took me at least 20-30 hours to get through, skipping only the very latter section on compactess and doing at least two of the harder problems in each section; but I have very little experience with analysis, something I'm sure would have helped complete this and gain the corresponding intuition much more quickly. Again, great book and would highly recommend it for self-study of topology.

This is an entry level book about general topology (or point set topology). The book is written in a clear and well-organized manner, quite easy to follow. It's worth mentioning that aside from the rigorous statement of concepts/theorems, the author also made an effort to explain how and why people get there. This helps me gain the mathematical intuition about the topics, and hence gain better and structured understanding and make the topics really a solid part of my knowledge. The problems are quite gentle and proper for beginners. BTW, I am not majored in mathematics, but I feel quite comfortable going through this book. Quite pleasant reading experience.

The book was ideal for an undergraduate looking to prepare for classes that would benefit from an understanding of Topology. It's a small book that holds up well and fits easily in even the tightest of backpacks.

Well, a simple language and very easy to understand. Edition is very small and you can carry it anywhere. You will need of course, a previous knowledge of mathematics to understand the great part of this book, but this is topology, ones of the fields more difficult in mathematic, even the more easy handbook will seem very high abstracted book if you doesn't know anything about theory of sets and functions. For students and mathematics is really a good point to begin a review of Topology, not the great only one book, but a start point to familiarize with terminology before to study Topology applications. I like this one.

book as described shipped promptly

The book is a very basic book on topology. It is very readable. You do not need to be a "great" mathematician to read this book. The references are good too. But, the reference are older books. I have read some of his references. I will use the book to help a person learn topology. It will get him started. Also, each chapter has one main topic, which is very nice. And, another good thing about the book is that it has a reasonable amount of pages.

After working in industry, I started grad school in control theory. As expected, I realized that I needed to fill a lot of basic concepts on point-set topology to further understand many of the proofs found in prestigious conferences and journals. This book, so ideal for self-study, helped me understand those basic concepts I was lacking!!! I highly recommend it for self-study...it is easy to understand and written in a pretty didactic way!

With all due respect to the late Professor Mendelson, I have struggled with this book. Having said that, I am neither a mathematician nor graduate student of same. I am a professional specialising in theory and am trying to teach myself (with MIT's help) some belated applied maths useful to theory making. For work I have embarked upon recently I am in need of upgrading my knowledge of things like abstract algebra and topology. This is one of the texts I purchased for self-study. I guess my main gripe is the book is a bit too dry for me. Which led to a lack of clarity on certain topics. I need a bit more flourish of explanation than mere definitions, theorems, examples. Over and over again. But I know, on the other hand Prof M wrote it from his lecture notes, for his students of serious maths. Not for me. So be it. For example, after reading the book through, then pouring over it in selected areas and chapters for weeks, re-visiting things I had not quite grasped, I still cannot tell the difference between a topological space and a topology - other than by theorem definition. Sure, there I can see (X,T) (T being curly T or whatever it is called) is the former, and T itself the latter. But I remain in desperate need of help from an author saying what this means. In clear simple English, preferably. I am not negative about the book as a whole, for I now know something at least about topology. As opposed to before I bought it and read it - when I knew zilch. Recommended for mathematical students; not for inquiring minds of applied people like myself who need more gently, gently.

If you are doing a module in metric spaces or topology you ought to read this, cover to cover ('cept maybe the first chapter, but this is always the case! Chapter 0 is never interesting) in your first or second year, you should know all the content (like the back of your hand) if you are doing a third year module. It is a brilliant introduction to everything you will need but is just that - an introduction. There's a superb amount of "hand-holding" in the proofs which I found really useful to boost my confidence, after that I'd start covering proofs and then checking them. This is good! I completely recommend this book, but I do not recommend it is your only topology book (There is another also called "Introduction to topology" with a blue over and an orange torus on the front, from Dover, this is not an introduction it is much more filled out and much faster, if you combine these two, with Munkres' Topology you're set) There is one thing I don't quite like, the treatment of Quotient topologies (or identification topologies) is rather weak and hard to understand, but I cannot write off a brilliant book due to an iffy 5 pages. I have no hesitation in recommending this book. I adore Dover because of the great prices also, I am getting quite the collection!

If you like structured thinking with a lot of abstraction thrown around, this is it! A feast for Math lovers.

O autor expõe com precisão e concisão cada capítulo. As demonstrações seguem uma abordagem axiomática bem suave.

The concepts are very thoroughly explained, and I like that the author started with a discussion of metric spaces before moving on to all the corresponding definitions in a topological space (open set, neighbourhood, etc). I would have liked more illustrations of examples to build geometric intuition though. The questions are also very good and help build a strong understanding of the section before, although there are no answers I have been able to find a pdf with all the answers in it for reference.

Easy read, with fairly OK exercises. One of the most gentle introductions to basic point set topology.