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| Topology (2nd Edition)
Hardcover
Edition: 2
Author: James Munkres
Publisher: Prentice Hall
Release Date: 2000-01-07
ISBN-10: 0131816292
ISBN-13: 9780131816299
List Price: $132.80
Average Customer Rating:
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Summaries and Customer Reviews are supplied by Amazon.com
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. Count ability 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.
Oh, no, not again.
| Customer Rating:  | Munkres has apparently forgotten the painful lessons learned in the 1950s and insists on reopening the Range War: does "range" mean the image (acceptable), the codomain (BAD idea), or both (total confusion)?
As a truly unforgivable sin against the succeeding generations of students, this renders the book UNACCEPTABLE for any purpose other than biofuel. |
,,,
| Customer Rating: | | 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] |
Ideal
| Customer Rating: | I've gone through most of this book and did many of the problems. The sections I skipped are the section on nets, the "review section" in chapter 4, the existence of a continuous nowhere-differentiable function, Dimension Theory, and all of Chapter 10 (Separation Theorems in the Plane), the Classification Theorem, and Constructing Compact Surfaces.
This is definitely my favorite math book. The two other books I've read this semester (Conway's Complex Analysis, and Rudin's Real and Complex Analysis) simply don't compare. In fact I'm afraid I'll always find fault with every other math book, after reading this one. There's alot of good expository prose, many examples and diagrams, and if you pay attention to details, and struggle to supply missing ones, you won't miss a beat and will succeed (unlike sometimes in Rudin's text). The problems are appropriate; very few are mindless, most do require a little thought, but a motivated student could solve most or all of them in a reasonable amount of time. There are no sudden breaks in proofs or in the text that are relegated as exercises (unless it's a repeat of a previous proof), and although results from previous exercises are sometimes used, he always states the necessary hypotheses. The book is self-contained - he begins with 70+ pages of naive set theory, for instance (not a prerequisite for the rest of the book).
I feel that reading this book and working its problems has given me a solid and comprehensive grounding in basic topology, and this book does go beyond what's usually taught in a first topology course, and the second half of the book is all algebraic topology. Here I found the review of abelian groups, free products and free groups to be extremely helpful, though I did still have to contemplate these alot on my own afterwards. The Seifert-Van Kampen theorem was also well-presented; he presents it as a pushout diagram. In the last chapter, as a nice application, he proves using linear graphs that subgroups of free groups are free.
I just simply love this book, but to be fair, I do have some minor qualms.
(1) There are a few obvious typos, and I didn't find more than six
(2) I believe one step in the proof of Lemma 68.9 is incorrect; this arises from a definitional issue of the subgroup generated by a subset. earlier, he assumed the subset was itself a subgroup, but now he's assuming it's arbitrary. the correct definition is on the next page, and the method of proof, with this definition, does give the right result; almost nothing changes in the proof
(3) In Theorem 68.4, the monomorphism and generating assumptions aren't necessary
(4) Problem #2 on page 438: I think the X_i should be path-connected, and Wikipedia is in agreement with this. I tried passing to path-components, which solved one problem but gave me others. On the other hand, if you assume path-connectedness, the proof is is the right level of difficulty.
(5) He gives an exercise regarding absolute retracts and adjunction spaces. I think he should've elaborated more on adjunction spaces, as it does involve new notions (e.g. free/topological union). Also his definition of adjunction space is incomplete, as compared to other definitions I found
(6) The book binding is horrible (it's the same with his other book, "Analysis on Manifolds"). If you're paying 100+ dollars for a book, you should expect to receive something very pretty, but the typesetting of this book is quite dull, and the book falls apart easily (mine is in many pieces).
In conclusion I highly recommend this book for self-study, and for seeing how math books can and should be written. I hope Munkres writes more textbooks, I'd read every single one of them.
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Good for auto-didacts
| Customer Rating: | | 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 ([...]). |
First half is great, don't bother with the second half
| Customer Rating: | | There are 14 chapters in the book, but it is only known for the first 8. The first 8 chapters cover pretty much everything you ever wanted to, or will ever need to know for point-set topology. It's easy to read, makes sense, lots of examples, proofs, and doable exercises. Extremely thorough. Munkres likes to talk, and some of his informal language is pretty funny in some places. Go somewhere else for Algebraic Topology. Some basics on homotopy theory are here, but nothing at all on (co)homology. My main complaint about this book is that it fails to make topology as exciting as it really is. |
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