Customer Reviews

Topology; A First Course

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

 

 

This is probably the best textbook on point-set topology (or general topology) ever written. Munkres is an excellent expositor. The book does demand a certain maturity; the definitions of a topology, a compact set, and a continuous function are quite unintuitive, and Munkres gives only a limited amount of motivation for them. Students with no experience with topological concepts in the context of, say, metric spaces will likely get lost quickly. But the more difficult theorems (e.g., Urysohn's Lemma, the Tychonoff theorem, and the Jordan curve theorem) are explained and proved very carefully in a "student-friendly" way. The book is also great as a reference, although some basic topics of importance to analysts are skimped on or omitted (Kelley's book "General Topology" will most likely have anything you can't find in Munkres). This book does not really discuss algebraic or geometric topology (besides a discussion of the fundamental group and covering spaces), which for most people are the really interesting parts of topology. Luckily, Munkres has written another book, "Elements of Algebraic Topology," which at least partially meets that need.

This has to be the best textbook I've ever had for a class. Munkres is very clear and *detailed* in his proofs. Sadly, many authors skimp the details or brush aside technical difficulties, leaving the reader to fend for themselves. Even in chapter 8, when he actually relaxes and does a few 'picture proofs', he fills in more of the gaps than other authors, like Massey, do when covering homotopy, fundamental group etc. His detailed proofs provide a good role model for when you're doing the exercises.

But this detail does not obfuscate matters. Munkres remains understandable. On the harder proofs he usually breaks things up into several steps, which keeps things readable. His examples are interesting, and his exercises range from easy to extremely difficult; actually most of them are of medium difficulty/somewhat hard variety.

I really feel that I'm getting a good understanding of topology in my topology class, mainly because of this book. The challenging exercises give me confidence that my feeling is based on some actual fact. All in all, a good experience. Hmmm...I guess I better finish reading the proof of the Jordan Curve Theorem. And get cracking on those homework problems.

This was my first introduction to point set topology as an undergraduate, and I enjoyed reading it even before taking the course.

Although not a hot research topic (compared to the rest of topology), it is foundational and as such many have assumed that point set topology could only be presented as a dull prerequisite for more interesting mathematics. Munkres' book, though, treats it as a goal of itself, as a fun world to play in, and as such, has attracted many students to topology.

It is recommended that a student first learn about metric spaces in a first-year undergraduate analysis class before learning about point set topology. Although the material is self-contained, the motivations for the definitions are hard to understand without knowing the more mundane examples.

Ordinarily, independent studies in mathematics courses are difficult. I found that Munkres' book well explained the topics of point set topology (up to chapter 8) and algebraic topology (chapter 8.) His exercises, for the most part, departed from the given examples and theorems, making them more challenging, but doable.

I would give this book 10 stars if I could!

Many books, especially those in the more theoretic regions of upper level mathematics are difficult to read, let alone use as a self-study text. The truth is that there is no real need for an instructor when using this book. The only book that I think may be its equal or better is Griffith's book on Electro-Magnetics.

I have studied a great deal of mathematics, and I wish all the books I have laerned from (or tried!) were written HALF as well as this one.

The content includes most, if not all, regions of fundamental point-set topology. There is next to know differential or algebraic topology, but there are other texts for that. The illustrations are extremely helpful (and I am not even a visual learner!). It would be difficult to give too much praise to this book, which is as comprehensive as it is lucid.

If you are teaching yourself topology, this is the only book to use.
Prof. Munkres has a gift for explaining the concepts and proofs. After you pick up the basics, you should look at Counterexamples in Topology by Steen and Seebach.

Maybe it's just good in comparison to my professor's very disorganized lecture notes, but I found this a very good resource to the material so far. Admittedly I'm only up to Chapter Three and a lot of that is review, but it provides some useful counterexamples as regards connectedness, path-connectedness, etc. One caveat is that if you're looking for this as a used (and cheap) alternative to the new edition, a small handful of the problems don't line up, so try and ask a classmate to double-check the assignment if you can.

Topology is a very beautiful subject, as many mathematicians will tell you. Point-set topology, the material which makes up the first five chapters of this book, however, is closely related to real analysis, and thus (in my humble opinion) quite dull. Nevertheless, Munkres does manage to make the study of point set topology bearable, and, in retrospect, possibly fun; the exercises consist of puzzles which are quite pleasant, if sometimes excruciating. Munkres treatment of algebraic topology is cursory and does not do justice to the subject; Massey's book would be a better introduction. This is a standard text, but make sure that you buy a simpler one if you are studying by yourself.

I am a grad student and wow, this is unbelievable. Some of the notation is inconsistent and all the problems are difficult. I am taking the class during the summer and it is a 24-7 ordeal.