Amazon.com: Customer Reviews: Introduction to Topology: Third Edition (Dover Books on Mathematics)
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Customer Reviews

4.4 out of 5 stars56
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on December 18, 2015
Overall, great introductory book to topology. The pedagogy was excellent and the development of topics <i>made sense</i> in going from metric spaces (a notion that is general more intuitive) to abstract topological spaces.

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.
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on May 19, 2009
I'd like very much this book. The book is very conceptual and also rigorous. It is self-consistent and this facilate his study. It progress step by step. If you need an Introduction, for self study this is a right book for starting. His writting style is very clear and the edition is also very good. The only defect I found is that there is no solutions for the excersices.
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on August 31, 2013
This book fills my desire to read some "real" mathematics, which I have always wanted to do. Though I am a physicist I never really got into the realm of pure mathematics. I picked the right book.
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on December 31, 2013
I found this book extremely helpful while working through chapters 2 and 4 of baby Rudin (along with Schramm's analysis book). There are numerous examples and accessible problem sets. In hindsight, I wish I would have worked through this book prior to taking my first course in analysis. This is also a great little book to work through prior to tackling the first half of Munkres. That it is an affordable Dover edition easily makes it a 5 star book.
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on October 11, 2014
Talk about concise and precise! Wish I had learned my topology through this book 45 years ago: I wouldn't have to relearn everything all over again. First chapter on set theory would have been worth the price of the book. A must for a beginner (the correct way to learn) or oldster (to correct his old learning).
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on September 25, 2011
This is a Wonderful book. I have my B.S. in Mathematics and I am in Graduate School for Mathematics. I am signed up for a Topology class next semester and to be ready, I picked up this, Introduction to General Topology by Cain and Topology by Munkres. Out of all of them this one presents Topology in the nicer way. Unlike in Munkres, it reads like a book, and unlike in Cain it doesn't assume steps and connections. This book provided the nice grounding for a more intuitive take on Topology by starting with Metric spaces and then linking everything from there. Cain then allowed for me to practice by giving me some examples and simple exercises. If there is one thing I would suggest to the author, put in some examples and some less general exercises.
Loved it and would suggest this book to anyone.
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on April 26, 2010
While this book is good, its a little overhyped. I did not particularly care for this book's presentation of connectedness and compactness (ie, the last two chapters), but the first three chapters were good. The problems in this book were also pretty good. They were at least interesting and difficult. However, there are no solutions, so it might not be the best book for self study. I personally think introduction to topology by gamelin and greene is better. These books should be used in conjunction with topology by munkres.
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on January 24, 2012
I had one semester of real analysis prior to picking up this book. I found it's presentation of metric spaces OK, though Mendelson seems happy enough with abstract definitions that he doesn't always try to help with developing some intuition. This book is probably pretty hard to read if you're not familiar with metric spaces.

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.
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on March 3, 2012
I enjoyed this book. It is a nice introduction to topology for undergraduates. It presupposes very little mathematical background. It is clear and well-written. Chapter 1 is a good introduction to set theory, Chapter 2 to metric spaces, Chapter 3 to topological spaces, Chapter 4 to connectedness, Chapter 5 to compactness. There are many exercises given. But I have one big problem with this book as a self-study guide: answers to the exercises are not provided. So I give it only 4 stars.
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on October 26, 2010
For all those who want to get into the field of Topology and then do Differential Geometry and then do General Relativity. Take this book as your first step to your final destination!
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