Rating: 
Summary: Clear Elementary Exposition
Review: 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.
Rating: 
Summary: Greatest math textbook I've read
Review: 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.
Rating:
Summary: Flawless introductory topology text
Review: 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.
Rating:
Summary: Flawless introductory topology text
Review: 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.
Rating:
Summary: One of the best math textbooks I know
Review: 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.
Rating:
Summary: Excellent introduction: makes point set topology fun
Review: 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.
Rating: 
Summary: A standard introductory topology book.
Review: 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.
Rating:
Summary: Excellent for either reference or self-teaching
Review: When I was in a topology course in graduate school, I constantly returned to the Munkres book to get clearer explanations of concepts than any of the graduate-level books could provide. What is noteworthy is that the ease of understanding did NOT come at the price of shallower coverage or lack of mathematical rigor. Although this is an undergraduate text, it covers almost everything you would get in a first-year graduate course in point set topology. If you want to learn that material for the first time without an instructor, then this is the book to use. And, if you are working in another area of mathematics, and come across words like "compact", "metric space", or "connected", and have forgotten what they mean, go straight to Munkres. He always talks to you like a real human being.
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