Introduction to Topology: Third Edition: ix (Dover Books on MaTHEMA 1.4tics)

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!

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.

Nice book, very entertaining. I am only on the second chapter ( on metric spaces ) but am finding it interesting enough that I am staying up late reading it. It is very well written and clear. I have minimal mathematical background ( just a little calculus and linear algebra ) and and sadly lacking in knowledge of analysis, but still find this book understandable. This is well worth the modest cost. Heck, this is worth ten times the modest cost !

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.

A useful book to help with learning Topology which is useful for a mathematics student! Have used this book almost everyday since buying it as it is easy to follow and understand. Has examples and explanations which are really useful.

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 5 Layout / Formatting (in the KINDLE edition): 1 or 2.

Definitely a fan of this book.

If you like structured thinking with a lot of abstraction thrown around, this is it! A feast for Math lovers.

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.

O autor expõe com precisão e concisão cada capítulo. As demonstrações seguem uma abordagem axiomática bem suave.

The concepts are very thoroughly explained, and I like that the author started with a discussion of metric spaces before moving on to all the corresponding definitions in a topological space (open set, neighbourhood, etc). I would have liked more illustrations of examples to build geometric intuition though. The questions are also very good and help build a strong understanding of the section before, although there are no answers I have been able to find a pdf with all the answers in it for reference.

Easy read, with fairly OK exercises. One of the most gentle introductions to basic point set topology.