Customer Reviews

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

5 star:		(5)
4 star:		(2)
3 star:		(2)
2 star:		(0)
1 star:		(0)

 

 

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.

This is the usual text for introductory Topology at UCLA, where I took the course. The authors (who teach at UCLA) have "if you haven't chewed through every syllable you are not learning" mentality. In short, the book is terse and demands a lot from the reader. Looking back, this was great preparation for graduate school and is probably the best philosophy for the serious undergrad. The book contains all of the information one needs for an introductory course, but absolutely no more. Not a single character is wasted on "extraneous" explanation. Be ready for battle when opening this one, but it's worth it.

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.

The exposition, while clear and not without attention to subtleties of the theory, is a little scattered. The metric spaces chapter is very good, but after that, it goes downhill. In particular, I was pretty disappointed that the mean value theorem was not proved as an application of connectedness. Everybody sees the mean value theorem in calculus, and the proof is really quite elegant. Also, a lot of important notions in topology are relegated to the exercises, and the rest of the exercises are like applications to analysis. It's kinda nice to be challenged to see the definitions in multiple ways through the exercises, but it would be nicer to get all the perspectives in the exposition, and be given exercises that would deepen one's understanding of the material.

All in all, this book feels like "topology as a branch of analysis" and only helps the reader to develop a modest working topological intuition. For readers interested in topology as its own subject, Munkres' book is the only book. For those readers desiring a more introductory approach, I found Mendelson's book to be an excellent introduction - the chapters on connectedness and compactness are thorough and quite helpful - though that book is lacking in that it doesn't discuss separation axioms at all, and contains few exercises. But that book is unique in that it despite its brevity it touches on metric spaces, categories, and the fundamental group.

If you're going to read this book, get a copy of Mendelson's book - it will flesh out your understanding of topology.

This book is divided into two parts: an introduction to topology, using metric spaces to motivate the definition of a topological space, and the algebraic applications of topology (such as homotopy theory and Jordan's theorem). The good things about it is its strong geometrical flavor and short and to-the-point explanations, which are nevertheless very good. Another excellent thing is the large number of exercises, most of which have full solutions (!) and/or hints at the end of the book. The chapter on metric spaces is also very informative, and stresses the many uses these spaces have in mathematics. However, the book does not really go into detail, especially when dealing with topological spaces. This is fine if you're looking for an introduction to topology (as the name implies . . . ) but it makes the book unsuitable as a reference. All-in-all a very "cute" book - as cute as introduction-to-topology books get!

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 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.

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.

This text has a thorough introduction to topology, especially as it is related to analysis. With several exercises (complete with solutions for the Dover edition), this text provides good practice and forces the reader to work out some of the main ideas. However, as stated in the book's preface it is lacking in examples. Even with the plethora of exercises, the lack of examples in the text makes the book quite dense. The book essentially becomes theorem, proof, theorem, proof etc. without reprieve which becomes difficult to read after not too long. I am planning to use this book along with Munkres' which I checked out from the library. It seems like this combination should be helpful.