Rating: 
Summary: Excellent for self-study
Review: (note: This applies to the 1974 edition. I'm guessing that the newer edition is similar or better) I've taught myself all the mathematics that I know beyond basic arithmetic, so I know what a good book for self study is. This is it. Munkres has a way of writing which makes a concept very clear, without losing rigor. I find that I only need to re-read sections in this book a couple of times to get them (as opposed to my customary 4-5). The examples and excersizes really helped me understand a number of key concepts. He follows a method suggested by Gian-Carlo Rota: give non-examples. He gives examples of connected but not path connected spaces, and similar things thoughout. Paul Halmos has said that one cannot really understand what a thing is until one has seen pathological cases, and Munkres gives many of these. I highly recommend it!
Rating:
Summary: Wonderful! Easy to understand.
Review: A lot of the concepts in topology are very abstract and not easy for students to grasp. But this book is broken down into enough small section to make it easier to learn topology's many new concepts a bit at a time while still learning all the important theorems and definitions. The exercises range well from simple and demonstrative to problems that require a lot of thought and full proofs. It worked well in my course on topology, but I imagine it would have been an easy book to use outside of the classroom or for independent reading as well.
Rating:
Summary: The best place to begin studying topology
Review: 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 Most textbooks in this area either seem outdated or overly abstract.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.
Rating:
Summary: The best place to begin studying topology
Review: 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.
Rating:
Summary: A Clear and Illuminating Exposition
Review: As an engineering physicist trying to pick up more abstract math, I found topology to be a very difficult subject. However, the professor's great insight and Munkres clear, complete, and precise work made the topic quite enjoyable. Munkres' greatest strength is his ability to organize well so that concepts are easier to understand. Furthermore, his use of examples are excellent in conveying the absract. There is always motivation provided so that theorems don't appear for no reason. In short, there is always a direction and a goal in mind which imparts a great sense of understanding once all in said and done. Sometimes there a too few exercises and the end of the sections. Other than that there is very little to complain about. It is an excellent book for introductory topology.
Rating:
Summary: A Clear and Illuminating Exposition
Review: As an engineering physicist trying to pick up more abstract math, I found topology to be a very difficult subject. However, the professor's great insight and Munkres clear, complete, and precise work made the topic quite enjoyable. Munkres' greatest strength is his ability to organize well so that concepts are easier to understand. Furthermore, his use of examples are excellent in conveying the absract. There is always motivation provided so that theorems don't appear for no reason. In short, there is always a direction and a goal in mind which imparts a great sense of understanding once all in said and done. Sometimes there a too few exercises and the end of the sections. Other than that there is very little to complain about. It is an excellent book for introductory topology.
Rating:
Summary: Wonderful text in a poor binding
Review: As far as contents is concerned, this is a wonderful textboot for self-studying topology. Full of examples and a bit slow-paced, it describes even the 'clever' proofs (like Tichonoff's theorem) so that it makes their core ideas come naturally. The selection of topics is superb (algebraic topology has a much wider coverage than in the 1st edition). The only drawback, and it is a serious one, is the binding. For a well-selling book $[...] worth, one could expect a *decent* binding, but the outcome is a *shame*. With time, the covers of my copy got ridiculously bent outwards, quite like if was cooked in my oven (which I didn't, of course).
Rating: 
Summary: Would be better iff....
Review: I am a grad student and wow, this is unbelievable. Some of the notation is inconsistent and all the problems are difficult. I am taking the class during the summer and it is a 24-7 ordeal.
Rating:
Summary: The Best Math Book I've Ever Read
Review: I have a fairly large library of mathematical litterature, and the Munkres book is, by far, the best book in my collection. If I were stranded on a desert island and could only have one book with me, it would be this one. The writing is always clear and the examples illuminating. An effort is also made to name theorems and lemmas in a useful way. It's much easier to remember things like "the tube lemma" and "the pasting lemma" than "theorem 3.4.553" My only qualm with the book is that the (excellent) exercises have no solutions - but then again, that is a failing of most topology texts.
Rating:
Summary: The best rigorous introduction to general topology!
Review: I have owned the 1975's first edition (red cover) of this book which I am currently studying again to pass a Ph.D. qualifying exam on topology. From the many topology texts that I have come across over the years, this one easily stands out as the best rigorous introduction to point set topology for a beginning graduate student. It covers all the standard material for a first course in general topology beginning with a chapter on set theory, and now in the second edition includes a rather extensive treatment of the elemantary algebraic topology. The style of writing is student-friendly, the topics are nicely motivated, (counter-)examples are given where they are 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 8 in the first edition). A notable minor issue in the first edition was the consistent usage of the pronoun "he" in the discussions for addressing all the possible readers of the book. (This fortunately has been modified in the 2000's edition.) On another note, I wish there were some hints & answers provided at the back of the book to some of the harder problems, so as to make this text more helpful for those of us who use it for self-study.
One of the two spotlight reviewers has correctly mentioned that Munkres does not cover differential topology here. I speculate this is perhaps because Munkres has already a separate monograph on differential topology. It is also necessary to get a handle on some fair amount of algebraic topology first, for a full-fledged coverage of the differential treatment. Regardless, one great reference for a rigorous and worthwhile excursion into differnetial topology (covering also Morse Theory) is the excellent monograph by Morris W. Hirsch, which is available on the Springer-Verlag GTM series.
At the end, I shall mention that one other very decent book on general topology which has unfortunately been out of print for quite some time is a treatise by "James Dugundji" (Prentice Hall, 1965). The latter would nicely complement Munkres (for example, Dugundji discusses ultrafilters and some more of the analytic directions of the subject.) It's a real pity that the Dover publications for example, has not yet published Dugundji in the form of one of their paperbacks.
|
