Introduction to Topology: Third Edition (Dover Books on Mathematics)

I am a robotic scientist in South Korea. I purchased this book for an introductory course in topology. As a non-specialist in applied mathematics, this book has concise contents and very readable. I am still on my way through this book and recommend this book to who wants to dive into an astonishing world of topology. Highly recommended for non-math-specialists.

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.

This is an entry level book about general topology (or point set topology). The book is written in a clear and well-organized manner, quite easy to follow. It's worth mentioning that aside from the rigorous statement of concepts/theorems, the author also made an effort to explain how and why people get there. This helps me gain the mathematical intuition about the topics, and hence gain better and structured understanding and make the topics really a solid part of my knowledge. The problems are quite gentle and proper for beginners. BTW, I am not majored in mathematics, but I feel quite comfortable going through this book. Quite pleasant reading experience.

The book is a very basic book on topology. It is very readable. You do not need to be a "great" mathematician to read this book. The references are good too. But, the reference are older books. I have read some of his references. I will use the book to help a person learn topology. It will get him started. Also, each chapter has one main topic, which is verynice. And, another good thing about the book is that it has a reasonable amount of pages.

It is a very good introduction to topology. There are so many examples for making out. I really recommend it. Enjoy itRemarkable

Well, a simple language and very easy to understand. Edition is very small and you can carry it anywhere. You will need of course, a previous knowledge of mathematics to understand the great part of this book, but this is topology, ones of the fields more difficult in mathematic, even the more easy handbook will seem very high abstracted book if you doesn't know anything about theory of sets and functions. For students and mathematics is really a good point to begin a review of Topology, not the great only one book, but a start point to familiarize with terminology before to study Topology applications. I like this one.

After working in industry, I started grad school in control theory. As expected, I realized that I needed to fill a lot of basic concepts on point-set topology to further understand many of the proofs found in prestigious conferences and journals. This book, so ideal for self-study, helped me understand those basic concepts I was lacking!!! I highly recommend it for self-study...it is easy to understand and written in a pretty didactic way!

A very enjoyable book to learn about the basics of topology. The author explains the subject matter in a very clear language for those who are beginner learners in Topology. I highly recommend it because I was very frustrated in other books.

This slim tome was my first formal encounter with topology, and I found it reasonably easy to work through on my own. Like many undergrad textbooks, it states that there are no prerequisites other than comfort with proof based maths. However, I would recommend making yourself familiar with basic analytic concepts and being comfortable proving theorems using them before starting the book. While none of this knowledge is strictly necessary for the book, an "analytic way of thinking" will be a helpful springboard into the material, as most of the new concepts covered in the book are presented as generalisations of concepts in Euclidean n-space.It starts off covering the basics of set theory and functions, most of which can be safely skipped by anyone with a semester or two of undergrad under their belt, and merely used as a reference (though it would be a good idea to look at the bit about commutative diagrams for those studying at that level). Chapter 2 covers metric spaces, giving definitions of open sets, neighbourhoods and continuous functions between metric spaces (among other things) in terms of open balls, then linking these concepts through various theorems. Chapter 3 defines topological spaces, then defines various concepts on topological spaces using the by now familiar analogous concepts in metric spaces. Readers may notice that many of the definitions given in Chapter 3 are almost word-for-word copied from theorems in Chapter 2, by design. Chapter 4 introduces the various forms of connectedness, and investigates homotopic paths & the fundamental group, though it doesn't seem to give a formal definition of the FG anywhere. Chapter 5 introduces compactness of both topological spaces and metric spaces, relating this back to material in chapters 2 and 3.While the exposition is mainly clear and concise, the book is somewhat light on examples in places and occasionally skips over some steps in examples which are not necessarily obvious to a first-time student of topology. The exercises are interesting, useful and have a good difficulty curve between the start and end of a section. The ink is a bit light in some places, which may make it difficult to read, but this can be forgiven due to the inexpensiveness of Dover books in general. While it lacks the depth and scope of weightier tomes such as Munkres, it lives up to its title, and makes a good, cheap first pass at a famously difficult subject.

If you are doing a module in metric spaces or topology you ought to read this, cover to cover ('cept maybe the first chapter, but this is always the case! Chapter 0 is never interesting) in your first or second year, you should know all the content (like the back of your hand) if you are doing a third year module.It is a brilliant introduction to everything you will need but is just that - an introduction. There's a superb amount of "hand-holding" in the proofs which I found really useful to boost my confidence, after that I'd start covering proofs and then checking them. This is good!I completely recommend this book, but I do not recommend it is your only topology book (There is another also called "Introduction to topology" with a blue over and an orange torus on the front, from Dover, this is not an introduction it is much more filled out and much faster, if you combine these two, with Munkres' Topology you're set)There is one thing I don't quite like, the treatment of Quotient topologies (or identification topologies) is rather weak and hard to understand, but I cannot write off a brilliant book due to an iffy 5 pages.I have no hesitation in recommending this book. I adore Dover because of the great prices also, I am getting quite the collection!

Excellent

This review is regarding the Kindle version specifically.I have no problem with the content of the book - and would give the book a 4 or 5 for content. However, the layout and formatting in the Kindle edition is absolutely appalling! It almost (almost - but not quite) renders parts of the book unreadable. Another reviewer mentioned the same problem.Summary ...Content: 4 or 5Layout / Formatting (in the KINDLE edition): 1 or 2.

I've recently finished my MPhys in Theoretical Physics, and going to start a Ph.D in Maths. I bought this to get to grips with topology, as I've had no previous exposure and really like the Dover series, I bought this one based on the reviews.The book is structured into manageable chunks, and the topics are very well explained, with lots of questions this book is vital for either studying topology, either self study or as a course supplement.