- Series: Dover Books on Mathematics
- Paperback: 224 pages
- Publisher: Dover Publications; 3 edition (July 1, 1990)
- Language: English
- ISBN-10: 0486663523
- ISBN-13: 978-0486663524
- Product Dimensions: 5.4 x 0.4 x 8.4 inches
- Shipping Weight: 9.1 ounces (View shipping rates and policies)
- Average Customer Review: 4.4 out of 5 stars See all reviews (63 customer reviews)
- Amazon Best Sellers Rank: #25,588 in Books (See Top 100 in Books)
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Introduction to Topology: Third Edition (Dover Books on Mathematics) 3rd Edition
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From the Back Cover
Unabridged Dover (1990) republication of the edition published by Allyn and Bacon, Inc., Boston 1975.
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Top Customer Reviews
Readers would be well advised to be familiar with the elements of proof, set theory, linear algebra, and abstract algebra in addition to analysis. A knowledge of geometry is also helpful, as one might expect.
Weighing the price of this book against the depth and breadth of other texts, this volume offers more to the student who is studying topology on a budget. Unfortunately, as with most books in this category, there is no solution guide provided for the exercises. A selection of hints for the exercises would have been a nice addition but otherwise does not detract from the purpose of the work: to give the beginning topologist an overview of the subject.
In particular, it was great for self-study as Mendelson doesn't shy away from fully fleshing-out proofs and repeating relatively similar cases with some additional notes (e.g. when going from metric to topological spaces and proving several ideas there). The book itself can certainly be read by anyone with a set theory background and some intuitive notion of limits/sequences (i.e. a class in pre-calculus), but that doesn't mean it's easy, <i>by any means</i>. I struggled quite a bit with the intuition behind some of the proofs, and have, more than once, rolled around on my bed trying to recall (or prove again) some particular statement that I found quite useful. Sadly, the book doesn't have a section on homotopy equivalence and some other useful notions, but do recall it is an introduction in exactly 200 pages of short text.
This book took me at least 20-30 hours to get through, skipping only the very latter section on compactess and doing at least two of the harder problems in each section; but I have very little experience with analysis, something I'm sure would have helped complete this and gain the corresponding intuition much more quickly.
Again, great book and would highly recommend it for self-study of topology.
I guess my main gripe is the book is a bit too dry for me. Which led to a lack of clarity on certain topics. I need a bit more flourish of explanation than mere definitions, theorems, examples. Over and over again. But I know, on the other hand Prof M wrote it from his lecture notes, for his students of serious maths. Not for me. So be it. For example, after reading the book through, then pouring over it in selected areas and chapters for weeks, re-visiting things I had not quite grasped, I still cannot tell the difference between a topological space and a topology - other than by theorem definition. Sure, there I can see (X,T) (T being curly T or whatever it is called) is the former, and T itself the latter. But I remain in desperate need of help from an author saying what this means. In clear simple English, preferably.
I am not negative about the book as a whole, for I now know something at least about topology. As opposed to before I bought it and read it - when I knew zilch.
Recommended for mathematical students; not for inquiring minds of applied people like myself who need more gently, gently.
Mendelson introduces topological spaces very well, though, with lots of examples, counterexamples, and explanations of both. It's dense reading (though not open-dense, ha-ha) but it is worth it. Definitely a good first book on topology.