Topology (2nd Edition) (Hardcover)

by James Munkres (Author) "We adopt, as most mathematicians do, the naive point of view regarding set theory..." (more)
Key Phrases: lifting correspondence, reduced edge path, standard covering map, Proof Let, Seifert-van Kampen, Proof Suppose (more...)

Editorial Reviews

Product Description
This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

From the Publisher
A concise, detailed introduction to topology. --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Hardcover: 537 pages
• Publisher: Prentice Hall; 2 edition (January 7, 2000)
• Language: English
• ISBN-10: 0131816292
• ISBN-13: 978-0131816299
• Product Dimensions: 9.1 x 7.2 x 1 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars See all reviews (37 customer reviews)
• Amazon.com Sales Rank: #55,860 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

72 of 73 people found the following review helpful:

5.0 out of 5 stars Excellent for either reference or self-teaching, July 2, 2000

By	Stan Vernooy (Henderson, NV) - See all my reviews (REAL NAME)

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.

56 of 57 people found the following review helpful:

5.0 out of 5 stars Flawless introductory topology text, June 30, 2003

By	David Elder "elddm" (Boston, Ma United States) - See all my reviews (REAL NAME)

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.

55 of 59 people found the following review helpful:

5.0 out of 5 stars One of the best rigorous introductions to topology!, January 4, 2005

By	Farshid Arjomandi (California, USA) - See all my reviews (REAL NAME)

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 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). 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-&-trusted source of learning and reference for generations of mathematics students.

The thing that should be mentioned though is, one would wish there were more hints and answers provided, at the back of the book, so as to make the text more helpful for those readers who use it for self-study. Also the price tag is very high which would inevitably stop some students from buying their own copies and encourage instructors to choose some of the many-times cheaper topology titles readily available through the Dover publications. A reviewer here has correctly mentioned that Dr. Munkres does not include differential topology in his presentation. This is almost certainly because of the length consideration issue, given that he has already written a separate monograph on the topic. In fact, it's also necessary to get a handle on some fair amount of algebraic topology first (such as the notions of homotopy, fundamental groups and covering spaces), for a full-fledged treatment of the differential aspect. Regardless, one high-level reference for a rigorous excursion into the area (with introductions to the Morse and cobordism theories), is the title by Morris W. Hirsch, which is available on the Springer-Verlag GTM series. 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. Before I finish, let me mention that the undergraduate 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 as special order through The Thomson Learning, Singapore. This title is closely modeled in exposition and selection of topics on Munkres (and Willard for that matter), thus nicely serving as a prerequisite for either book.