Customer Reviews

Topology (2nd Edition)

5 star:		(23)
4 star:		(5)
3 star:		(1)
2 star:		(2)
1 star:		(1)

 

 

When I was in a topology course in graduate school, I constantly returned to the Munkres book to get clearer explanations of concepts than any of the graduate-level books could provide. What is noteworthy is that the ease of understanding did NOT come at the price of shallower coverage or lack of mathematical rigor. Although this is an undergraduate text, it covers almost everything you would get in a first-year graduate course in point set topology. If you want to learn that material for the first time without an instructor, then this is the book to use. And, if you are working in another area of mathematics, and come across words like "compact", "metric space", or "connected", and have forgotten what they mean, go straight to Munkres. He always talks to you like a real human being.

This is a fantastic book, the type of perfection to which all writers of mathematical texts should aspire. There are plenty of definitions, theorems, and proofs, as well as informative examples and prose exposition. The expository text is what makes this book really stand out. Munkres explains the concepts expressed abstractly in theorems and definitions. That is, he builds motivations for the necessarily abstract concepts in topology. This greatly improves the readability of the book, making it accessibly to general readers in mathematics, science, and engineering.

The book is divided into two sections, the first covering general, i.e. point-set, topology and the second covering algebraic topology. Exercises (without solutions) are provided throughout. The exercises include straight-forward applications of theorems and definitions, proofs, counter-examples, and more challenging problems.

My only complaint with this book is that it does not discuss manifolds and differentiable topology, but other texts fill this gap.

I highly recommend this book to anyone interested in studying topology; it is especially well-suited for self study.

I used to own the 1975 (first) edition of this title since the late 1990s, but quite recently purchased the new edition as well, and donated the old book to our campus library. Despite having very close similarity to the text by Stephen Willard (1970, Dover issue 2004) which points to the fact that both authors must have used the same source articles, Munkres's book stands out as one of the best rigorous introductions for a beginning graduate student. It covers all the standard material for a first course in general topology starting with a full chapter on set theory, and now in the second edition includes a rather extensive treatment of the elementary algebraic topology. The style of writing is student-friendly, the topics are nicely motivated, (counter-)examples are given where they were needed, many diagrams provided, the chapter exercises relevant with the correct degree of difficulty, and there are virtually no typos. The 2nd edition fine-tunes the exposition throughout, including a better paragraph formatting of the material and also greatly expands on the treatment of algebraic topology, making up for 14 total chapters as opposed to eight in the first edition.

I particularly found useful the discussion of the separation axioms and metrization theorems in the first part, and the classification of surfaces and covering spaces in the second part. In my opinion, after going through the discussion of algebraic topology in Munkres, the students should be ready to move forward to a (now standard) text such as Hatcher, for further coverage of homotopy, homology and cohomology theories of spaces. Eventhough a few contending general topology texts --such as a recent title published in the Walter Rudin Series-- have started to hit the academic markets, Munkres will no doubt remain as the classic, tried-and-trusted source of learning and reference for generations of mathematics students. This is despite the fairly high price tag which could stop some students from buying their own copies, hence encouraging instructors to choose some of the much cheaper topology paperbacks readily available through the Dover publications. Also the majority of the Munkres readers would have wished to see more hints and answers provided at the back so as to make the text more helpful for self-study. Those merely testing the waters in topology should try Fred H. Croom's 1989 text, since the latter is a more accessible title similar in the exposition and selection of topics on Munkres (and Willard for that matter), thus nicely serving as a prerequisite for either of the more advanced books.

A couple of ending remarks: A reviewer has correctly mentioned here that Dr. Munkres does not include differential topology in his presentation. This is because of the length consideration, given that he has already written a separate monograph on the topic. In fact it's also necessary to first get a handle on a fair amount of algebraic topology such as the notions of homotopy, fundamental groups, and covering spaces for a full-fledged treatment of the differential aspect. In any case, one high-level reference for a rigorous excursion into this area is the Springer-Verlag GTM title by Morris W. Hirsch which includes introductions to the Morse and cobordism theories. I'd also like to mention that another decent book on general topology, unfortunately out of print for quite some time, is a treatise by "James Dugundji" (Prentice Hall, 1965). The latter would complement Munkres, as for instance Dugundji discusses ultrafilters and some of the more analytical directions of the subject. It's a pity that Dover in particular, has not yet published this gem in the form of one of their paperbacks.

My introduction to Munkres was in an independent study of point set topology in my final semester of undergraduate work. A professor assigned me problems from the book, but my learning was largely self motivated. I found that it was an excellent book for independent study. The text was clear and readable and the exercises helped to cement the concepts that are introduced in the reading.

Later at graduate school, Munkres was also used in a topology class at the beginning graduate level. Highlights were taken from the first section (point set topology), and a large focus of the class was on the algebraic topology in the second section of the book. Sometimes I had difficulty following exactly what the professor was doing at the blackboard, but I could always understand what was going on when I consulted Munkres.

I would stress that this is only to be used as an introduction to algebraic topology, as there is nearly no development of homology groups and other algebraic concepts. However, it gives a very good presentation for the fundamental group. As a whole it would be a very good addition to your mathematical library.

This is the standard into to point-set topology for a reason. It covers general topology very well, with easy-to-follow proofs and exercises that are actually possible to do. The problem is that the algebraic topology portion of this text (around 1/3 of the whole thing), is vastly inferior to Hatcher's "Algebraic Topology" book, which happens to be free. If you're looking for a good way to begin studying topology, then this is the book you're looking for, but if you want to learn about the fundamental group (and various related topics), then Allen Hatcher's book is available for free on his website. It calls to you...[insert spooky noises here]

I bought this book for my first course in point-set topology. I must say I was quite confused when I began the actual topology portion of the book (chapter 2), but this was due to the difficulty of topology, in general, and not the book itself. Looking back at the introduction to a topology, I can now see it was very good, as was the introduction to the various types of topologies. The rest of the book is almost a reference to the basics of topology with some plan of cohesion behind it. Unfortunately, this lack of a completely cohesive approach is unavoidable, since a course in point-set topology ought to provide a stepping stone one can use for further study in topology and not a mountain one can climb and conquer and thus know the subject completely. This requires that a cursory explanation of many ideas be presented.

Nevertheless, Munkres' book is quite readable and yet still rigorous. His exercises are very instructive in reinforcing the many ideas and provide a wide variety in problem difficulties for a motivated undergraduate in math.

If you are searching for a book that provides a friendly step-by-step aproach to learning point-set topology, I would not recommend this book for it would be too difficult. If you are searching for an introduction to point-set topology that will give you a solid grounding in the basics of point-set topology, but at the same time will give it to you in an easily approached manner, than this book is for you. It is my belief that this book is about as close a math textbook can come to being a "read in front of the fire" sort of book.

Although both parts of this book are exceptionally well written,
I've seen even better presentations of general topology in Sutherland's "Introduction to Topological and Metric Spaces", although admittedly Chapters 5 and 8 are not covered there. On the other hand I have found it very difficult to find a better book that covers part 2 of this book, Algebraic Topology. Most textbooks in this area either seem outdated or overly abstract. However, Munkres takes the time to explain concepts like covering spaces and the fundamental group with care and detail, providing a number of concrete examples. Combine this book with his differential topology book, and one can easily self-study his or her way to a mastery of first-year graduate topology.

This is the text that my first graduate level topology class is using. Over all I find it very well written. The author uses good examples for motivation and explaination of the topics he covers. The exercises are also well thought out and instructive. They're challenging enough to make you really learn the material, but not so hard as to sway the only average mathematician from the subject. I highly recommend this book, even if it's not for your class. It'll be a welcome reference book to add to your math text collection!

I used this book to teach myself some topology. Not being a mathematician, I cannot really assess how it trades off rigour with accessibility, but I can recommend it for self-study. It starts more or less from zero, is pretty clear and provides some welcome intuition to supplement the proofs. The best thing about it is the large number of challenging exercises, solutions to which are readily available on the web ([...]).

This is by far the best undergraduate mathematics textbook I have ever used. I was fortunate enough to have a very good professor for this course and combined with this book was quite possibly the best undergraduate mathematics course I've ever taken. This book is amazing for self study and is truly indispensable. Munkres' explanations are very clear and rigorous at the same time and the problems are very good. Of course, there is no solutions manual which is the only drawback if one is using this text for self study. There really aren't any other options if you want to learn topology for the first time. The book has a nice introduction to set theory then it covers point set topology and algebraic topology. I would recommend this book to anyone who wants to learn topology. I sure had a lot of fun reading through this book!