Topology (2nd Edition) Description:

Topology (2nd Edition) review:
5 stars (The best rigorous introduction to general topology!) - I used to own the 1975's first edition of this title since the late 1990's, but quite recently purchased the new edition as well, and donated the old book to our campus library. Before anything else, let me express that from the many topology texts that I have come across over the years, this one easily stands out as the best rigorous introduction 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 elemantary 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). A notable minor issue in the first edition was the consistent usage of the third person masculine pronoun in the discussions, specially in the foreword, for addressing all possible readers of the book, but this has fortunately been revised in the 2000's edition. 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-&-trusted source of learning and reference for generations of mathematics students.



The one thing that should be mentioned though, one would wish there were some more hints and answers provided, at the back of the book (at least to the harder problems), so as to make the text more helpful for those readers who use it for self-study. Also a reviewer has correctly mentioned here that Dr. Munkres does not include differential topology in his presentation. I speculate this is perhaps because he has already written a separate monograph on the topic. In fact, 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 the area (covering brief introductions to the Morse and cobordism theories as well), is the excellent title by Morris W. Hirsch, which is available on the Springer-Verlag GTM series. I would also like to 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, as for example, Dugundji discusses ultrafilters and some more of the analytical directions of the subject. It's a real pity that The Dover Publications in particular, has not yet published this gem in the form of one of their paperbacks. The undergrad students testing the waters for the first time, should try Fred H. Croom's text, originally published in 1989 but now again re-issued and available in limited numbers and/or special order, through The Thomson Learning, Singapore. This title is closely modeled in exposition and selection of topics on Munkres, thus nicely serving as a prerequisite.
5 stars (great!) - Not much to add here... there are enough easy problems that I can get the hang of something, but also some really tough ones at the end of each problem section. The proofs and examples in the text are really good guides to doing the problems also. In some sections there are counterexamples for, say, the converse of a theorem which are always really pathological. At the beginning of each section there is some discussion on what to expect, why the stuff is important, what to do with it, etc. Even though I had a really good prof for the topology course I did this book was very helpful out of the classroom.
5 stars (Excellent Topology Book) - 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.