Dover Introduction to Topology: Third Edition

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.

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.

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.