Customer Reviews

Topology

5 star:		(13)
4 star:		(2)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

Not much to add here... there are enough easy problems that I can get the hang of something, but also some really tough ones at the end of each problem section. The proofs and examples in the text are really good guides to doing the problems also. In some sections there are counterexamples for, say, the converse of a theorem which are always really pathological. At the beginning of each section there is some discussion on what to expect, why the stuff is important, what to do with it, etc. Even though I had a really good prof for the topology course I did this book was very helpful out of the classroom.

My introduction to Munkres was in an independent study of point set topology in my final semester of undergraduate work. A professor assigned me problems from the book, but my learning was largely self motivated. I found that it was an excellent book for independent study. The text was clear and readable and the exercises helped to cement the concepts that are introduced in the reading.

Later at graduate school, Munkres was also used in a topology class at the beginning graduate level. Highlights were taken from the first section (point set topology), and a large focus of the class was on the algebraic topology in the second section of the book. Sometimes I had difficulty following exactly what the professor was doing at the blackboard, but I could always understand what was going on when I consulted Munkres.

I would stress that this is only to be used as an introduction to algebraic topology, as there is nearly no development of homology groups and other algebraic concepts. However, it gives a very good presentation for the fundamental group. As a whole it would be a very good addition to your mathematical library.

As far as contents is concerned, this is a wonderful textboot for self-studying topology. Full of examples and a bit slow-paced, it describes even the 'clever' proofs (like Tichonoff's theorem) so that it makes their core ideas come naturally. The selection of topics is superb (algebraic topology has a much wider coverage than in the 1st edition).

The only drawback, and it is a serious one, is the binding. For a well-selling book $[...] worth, one could expect a *decent* binding, but the outcome is a *shame*. With time, the covers of my copy got ridiculously bent outwards, quite like if was cooked in my oven (which I didn't, of course).

This is a fantastic book, the type of perfection to which all writers of mathematical texts should aspire. There are plenty of definitions, theorems, and proofs, as well as informative examples and prose exposition. The expository text is what makes this book really stand out. Munkres explains the concepts expressed abstractly in theorems and definitions. That is, he builds motivations for the necessarily abstract concepts in topology. This greatly improves the readability of the book, making it accessibly to general readers in mathematics, science, and engineering.

The book is divided into two sections, the first covering general, i.e. point-set, topology and the second covering algebraic topology. Exercises (without solutions) are provided throughout. The exercises include straight-forward applications of theorems and definitions, proofs, counter-examples, and more challenging problems.

My only complaint with this book is that it does not discuss manifolds and differentiable topology, but other texts fill this gap.

I highly recommend this book to anyone interested in studying topology; it is especially well-suited for self study.

This book is extremely well written; a great place to start learning topology. Unfortunately, the publisher has not given it the binding it deserves. Look, an [expensive] hardbound book deserves a nice binding (with so-called "signatures," for instance), not a paperback glue binding that begins losing pages within weeks of gentle use. I took mine to a book repairman at my university library, who took one look at the poor thing and shook his head; there was nothing I could do: it was simply a cheap binding.

Although both parts of this book are exceptionally well written,
I've seen even better presentations of general topology in Sutherland's "Introduction to Topological and Metric Spaces", although admittedly Chapters 5 and 8 are not covered there. On the other hand I have found it very difficult to find a better book that covers part 2 of this book, Algebraic Topology. Most textbooks in this area either seem outdated or overly abstract. However, Munkres takes the time to explain concepts like covering spaces and the fundamental group with care and detail, providing a number of concrete examples. Combine this book with his differential topology book, and one can easily self-study his or her way to a mastery of first-year graduate topology.

This book should be treated as a senior undergraduate textbook on general probability. It can be used for 2-semesters 1st year graduate course textbook though it lack comprehensive cover of general probability, most notably significant weakness on set theory.
The strength is clarity of exposition which is quite rare in mathematics on this level. That makes this book easy to read but there will be many places where a trained topologist will notice the absence of serious treatment.

As an engineering physicist trying to pick up more abstract math, I found topology to be a very difficult subject. However, the professor's great insight and Munkres clear, complete, and precise work made the topic quite enjoyable.

Munkres' greatest strength is his ability to organize well so that concepts are easier to understand. Furthermore, his use of examples are excellent in conveying the absract. There is always motivation provided so that theorems don't appear for no reason. In short, there is always a direction and a goal in mind which imparts a great sense of understanding once all in said and done.

Sometimes there a too few exercises and the end of the sections. Other than that there is very little to complain about. It is an excellent book for introductory topology.

Taking a first course in topology could not be better complemented. This clear exposition of point set and algebraic topology is so well written that it could even be used for self study. Motivation from the professor is always helpful, but Munkres actually goes quite far in providing a reason for the topics in question. Furthermore, the examples clarify many of the presented concepts and even show some of the misconceptions a student may have.

Having a course in analysis would certainly make the book flow since otherwise it would just to be a mental exercise rather than an extension of familiar concepts.

The exercises are very well thought out and are meant to be solved by all students given that they have some diligence. They truly help in turning a fog of concepts into concrete understanding.

(note: This applies to the 1974 edition. I'm guessing that the newer edition is similar or better) I've taught myself all the mathematics that I know beyond basic arithmetic, so I know what a good book for self study is. This is it. Munkres has a way of writing which makes a concept very clear, without losing rigor. I find that I only need to re-read sections in this book a couple of times to get them (as opposed to my customary 4-5). The examples and excersizes really helped me understand a number of key concepts. He follows a method suggested by Gian-Carlo Rota: give non-examples. He gives examples of connected but not path connected spaces, and similar things thoughout. Paul Halmos has said that one cannot really understand what a thing is until one has seen pathological cases, and Munkres gives many of these. I highly recommend it!