Introduction to Topology: Second Edition

Introduction to Topology by Gamelin is a great book for starters. There are a considerable number of exercises with answer sugestions and most part of the material in the book is self contain. Thus, Introduction to Topology is a reference for those who are familiarising with this subject.

I highly recommend this book as a supplement to another topology text since it has a lot of hints and answers. Students may not learn very from it because they may just copy the answers in the back of the text. It is a great book though.

I wanted to teach myself some topology and a friend with mutiple Math PhD's reccomended this book to me. This is a tremendous value, and is comprehensible. But it is prety lean and direct, so be prepared to work on this in a quiet place where you can concentrate for a sustained period of time. Proofs are direct, and expect you to be familiar with notation through all of Algebra. I re-emphasize: there is zero, no, nada, blank, null coddeling here. Every single word, every single notation is important, and if you haven't read, marked, and inwardly digested each one it is a promise you will be lost in a page or two and have to go back. There is no fat here at all and the authors don't babysit you or expalin anything five different ways. This is direct on the coal face math. Still, I knew only basic basic basic totpology before this, and now I have a vague understanding of all the major areas of further inquiry. A very good value.

I used this book to teach myself the basics of point-set topology and homotopy theory. What makes this book so great is that the author doesn't waste words in delving into the heart of a concept, while providing insight into it. A good collection of interesting problems, most with solutions in the back of the book. This makes this book very good for self study. If you liked Rudin, you'll probably like this book as well, as it is written in a similar style. If someone knows of a better introduction, do let me know.

This is a lean fast introduction to topology at the third or fourth year level. Pure math types only. The book is terse but the topics are selected with care and one things leads to the next. The proofs are sufficiently detailed. Nearly every exercise has a solution in the back. The clearest exposition of the fundamental group I've seen.