Amazon.com: Topology (Dover Books on Mathematics): 9780486656762: Hocking, John G., Young, Gail S.: Books

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• 5.0 out of 5 stars The great topology classic, nicely printed

  Reviewed in the United States on November 13, 2024

  When I first studied topology in 1975, one of the most popular topology books was Hocking and Young. It's still an important classic. Recently I needed some information about wild arcs, and this was the only book with the required information amongst my collection of 20 topology textbooks. (See pages 176-177.)

  The first half of this book is about point-set topology, which is my main interest. The second half is about combinatorial topology, i.e. topological invariants of finite-dimensional manifolds. Most topology books are strongly focused on either point-set topology or combinatorial topology. So it's great to have a book which introduces both disciplines in as much detail as such a small book can give.

  While writing a book which covers point-set topology (several hundred pages), I have found very often that Hocking and Young gives me the nicest definitions and theorems to refer to. All of the basic theorems which every mathematician should know about point-set topology are here. The proofs are nice and the diagrams are very numerous, clear and helpful. The counter-examples are well illustrated and well presented. Not many topology books have as many diagrams as this book.

  Then in the second half (chapters 4 to 8), there is homotopy theory, a 25-page chapter on simplicial complexes, then simplicial homology theory and two more chapters on homology theory.

  It's a topology classic from 1961, but it's still the best all-round introduction to topology at the 3rd year University level.

• 5.0 out of 5 stars It gives a great proof that higher homotopy groups are abelian.

  Reviewed in the United States on May 21, 2023

  I purchased it for a project in alg top to do higher homotopy groups (of spheres) and the first theorem i had to prove was that pi_n(X) is abelian for n>1 but with pictures and explicit homotopies from each picture to the next. The Author did a great job at explaining the proof very self contained.
  

• 3.0 out of 5 stars Decent book with flaws

  Reviewed in the United States on November 3, 2007

  The book has its virtues, sure enough. But there are some downsides
  to it as well that I feel are underrepresented in the other reviews so far.

  Let me first note that, contrary to the statement of one other reviewer, there are exercises in this book, and not too few. However, I found that I did not need them, since thinking deeply about all the little flaws and omissions that are scattered through the text allowed me to mature faster than going through these exercises. Needless to say, though, that this type of exercise can be a bit frustrating. I often found myself wondering if it was my lack of maturity that made me struggle, or if the authors actually made their life too simple at various points. Luckily, I found amply evidence for the latter. For example, the reader familiar with homotopy may open the book on page 164 and inspect their proof that the curve given by f(1-x) is the inverse of that given by f(x) in the fundamental group. While this is a true statement of course, their constructed homotopy to prove this is not really continuous, and a slight modification of it could be used as a "proof" that every curve is homotopy equivalent to a constant one. A useful review of the book by a professional can be found at the following URL,

  [...]

  where similar shortcomings are noted. I agree that the latter will probably not slow down an expert who chooses this book as a reference. For beginners, however, they are unnecessary obstacles. I bought this book because I got attracted by the balanced selection of topics ranging from point set topology to algebraic topology. I wanted to learn the latter, but first needed to become proficient in the former. Having now read only the first part of the book devoted to point set topology, I can say that the book did its job, and did it quite well. However, I cannot shake off the feeling that I could have learned the same material in a fraction of the time from a different book. Feeling that I do now have a solid enough background in point set topology, I am considering to not read the second half of the book, and instead learn algebraic topology from a more modern text.

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• 5.0 out of 5 stars Very Impressed

  Reviewed in the United States on May 3, 2005

  I am teaching myself topology with this book right now, and I must say it has an excellent balance of motivation and rigor. The very first definition in the book reveals the implications of topology to anyone who has studied limit pts (and how connectedness is defined in terms of same). After less than a week of study, I understood the big picture better than most people I know who have taken a full course. The exercises are a little sparse, perhaps, but they generally make up for their small number with increased difficulty. I have only encountered a few exercises that I could call trivial. My only gripe is that the exercises are sometimes a little tricky to find.
  

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• 4.0 out of 5 stars Good...

  Reviewed in the United States on March 8, 2013

  A good text, but nowhere near the level of, say, Munkres. Still, it can have an interesting exposition, at times.
  

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• 5.0 out of 5 stars A Professional Topologist loves this book.

  Reviewed in the United States on December 6, 2001

  When I was a graduate student 40 years ago there were very few texts in topology. The only two that I recall being in use were Hocking and Young and the book by Kelley. Over the years my copy of Hocking and Young has become quite worn. It is a wonderful book that gives the true flavor of topology. It is also contains a large number of topics that one can refer to later on. It becomes quite apparent very earlier that no one will be able to fully appreciate the book in the time span of one course. It is a book that must be read and reread over and over again. It is a real classic. I do not believe that it is the type of book that would be of much or any general interest but to a point set topologist it is a classic and must for his bookself. I am quite surprised over its low price. I can not help but compare it with the newer book by Munkres. I recall seeing Munkres book many years ago and disliking it. But the current edition seems much closer in flavor to HY and Munkres book is quite good. Munkres style is much clearer than HY, but both books target a very specialized group of people. Neither book is for the faint of heart and will take many years to absorb. Considering that Munkres book is 9 times as expensive as HY, HY seems to be the better buy.
  

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