"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." |