Customer Reviews

Topology: Point-Set and Geometric (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

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4 star:		(1)
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2 star:		(1)
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Overall, this book was a wonderful introduction to the field of Topology. At times the author is a little cryptic, although it is hard not to be given the subject matter. Proofs are well-organized and documented and there is no shortage of them. This book offers a great introduction to Topology for any undergraduate with at least a background in Abstract Algebra and Set Theory.

I don't know what the other reviewer was smoking but it certainly must have been potent stuff.

In an effort to allow a broader audience to learn Topology Mr. Shick dumbs down the material to a level where it's almost useless. Almost all of the proofs follow from definitions, others from logical manipulation of already proved theorems e.g. contraposition (which doesn't belong in a class at this level), and very very few require actual construction. The most difficult problems, relative to the gag problems, have hints that all but give the solution. But most likely these won't even be assigned work!

What's most telling is that these most difficult problems are actually stolen (borrowed?) straight from Munkres' "A first course in Topology." Now that's fine when doing problems as homework because Shick is in effect weening us dummies onto these more difficult problems with hints. What's not acceptable is that Professors will then use problems from Munkres' book on exams with disregard for the fact that Shick's book only prepares you to solve such problems with the assistance of hints. And I don't mean psychologically either. There were several places where Munkres' development of the material included things that are not included in Shick's and yet the same problems were assigned at the end of the section.

Anyway even if you're studying this on your own, though the previous statements still are relevant, the book has other pedagogical flaws. The discrete and indiscrete topologies are used as examples for absolutely everything! In my opinion that provides nothing, other than a feeling of "geewiz". The same types of things are proven over and over again instead of being relegated to problems. "If (X,t) is _____ and A is a subspace of (X,t) then A is ____." Such and such is a topological property must've been proven in every chapter for at least twice.

And it's a first printing so there's publishing mistakes everywhere. The worst of which is that the index is 2 pages behind, meaning that if it says something is on page 68 then it's actually on 66.

Study from Munkres' book, the first chapter alone is worth more than this entire book. I hate to be mean but there's a reason why Mr. Shick teaches at John Carroll University and Munkres teaches at MIT. I greatly regret that my professor picked this book for our class. I give it two stars out of charity and pity for Mr. Shick's soul.