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.

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.