Topology

by James R. Munkres

This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

Genres: Mathematics, Textbooks, Science, Reference, Nonfiction, Technical, Philosophy

537 pages, Hardcover

First published June 1, 1974

Reviews

[Santaraksita]

Overrated and outdated. Truth be told, this is more of an advanced analysis book than a Topology book, since that subject began with Poincare's Analysis Situs (which introduced (in a sense) and dealt with the two functors: homology and homotopy).

The only point of such a basic, point-set topology textbook is to get you to the point where you can work through an (Algebraic) Topology text at the level of Hatcher. To that end, Munkres' book is a waste of time. There is not much point in getting lost in the thickets of the various kinds of spaces or their pathologies or even the metrization theorems. One can always come back to these later.

Lee's Introduction to Topological Manifolds is a much better book -- for one, its chapter on CW-complexes will make it much easier to follow Hatcher's Chapter 0.

[Matthieu]

After making my way through Dover's excellent Algebraic Topology and Combinatorial Topology (sadly out of print), I was recommended this on account of its 'clean, accessible' (1) layout, and its wise choice of 'not completely dedicating itself to the Jordan (curve) theorem'. (2)

I found it to be an even better approach to the subject than the Dover books. That said, they're all highly recommended. However, one new(er) to the concepts of algebraic and general topology will probably find this book to be more accessible, even if the algebraic treatment is too light to properly slake the gullet of a more seasoned topologist.

*/(1); (2): The CMU professor in charge of our summer program.

[Pietro]

This is *the* topology book for self-study. Extremely clear, full of examples. Assumes no background and gets *very* far: on the "general topology" front, does Uryssohn and Nagata-Smirnov metrization, Brouwer fixed-point, dimension theory, manifold embeddings. There's a huge section on algebraic topology which I've only skimmed, but looks similarly thorough.

[Arnar Ágúst]

Næstum komið ár síðan ég las þessa. Verð þó að viðurkenna að ég las ekki alla kaflana, komst ekki í gegnum seinasta þriðjunginn um það bil. Eins og JIM sagði er þetta sígildur texti. Ég vil nú sjálfur meina að Munkres og JIM séu eins og bjór og sígó; eða þjappað og Hausdorff. Þeir virka sem sagt mjög vel saman.

[Milad]

Best place to begin studying topology. The first unit is about some fundamentals that most of the people who intend to study topology, already know much about. The main goal of the book, teaching topology, mainly commences from unit two. !:)

[Jiachen Guo]

A very gentle book on topology. Excellent for a physics student.

[Ezra]

Good selection of exercises of different difficulties. I didn't find the writing to be very engaging. I don't think that the content he prioritizes are the most important things for someone trying to learn the basics of topology. If one is explicitly trying to learn about point-set topology, the extensive variety of different point-set properties, and all of the pathological examples, then this is four or five stars. But for an introduction to topology, this is really not what is important, and I give three stars.

[Rhys Tilford]

This class was really cool! I may have been banging my head against a wall once or twice (metaphorically) but I really do think I would enjoy it more if I learned more of it.

I gave a presentation at the end of the class and my visual aid was a webpage I built for my computer science class. Here's the link if you want to take a look: rctilford.github.io/personal-rhys-til...

I will warn you that the page isn't set up well for mobile phones.

[Alec]

Absolutely slaps.

Read chapters 1-3:
- Set Theory and Logic
- Topological Spaces and Continuous Functions
- Connectedness and Compactness

[Matthew Zabka]

Excellent book on point-set topology. The introduction chapter is also exceptional. I did as many exercises as I could out of this textbook as an undergraduate one summer, and I believe that doing so took my mathematical maturity to the next level.

[Liora Sophie]

Munkres is goofy as well as a good teacher. This book is readable and has excellent explanations. Well organized. I took it to class and made notes in the margins. An excellent introduction to topology.

[Ojas]

nice book on topology, challenging problems, but text is too wordy

[Mir Ibtisam]

good

[Arya Tabaie]

Beautifully written. Very rigorous and very human.

[Alek Frohlich]

Complete and well-organized book. Wasn't a fan of chapter 7, and its treatment of quotient topology is quite shallow and unmotivated.

[Didier "Dirac Ghost" Gaulin]

Munkres's Topology is a great overview and a solid introduction to the world of topology and an entry point into the world of algebraic topology is section 2. The author spends a fifth of the book on set theory and logic, which might not be necessary for the graduate student, hence, this is probably aimed as a last year subject for an undergraduate student. Munkres does not assume much of the student and explicate every subjects with a great deal of details, Venn diagrams and a large set of examples and questions to supplement the reader's ability to affirm and test his understanding. For the constructivists, some of the proofs might not be up to such framework, the acceptance of the axiom of choice might also irritate others, but all in all, they are well put and quite clear, for the most part. As someone who already had knowledge of the subject, I would probably pair this book with Introduction to Topological Manifold for someone who is learning on their own.

[Tommy Pett]

I read through chapters 1-4 thoroughly and skimmed the rest of the point-set sections, and I struggled a lot with this text even though nothing he says is fundamentally *that* bad. I think I might be better off now than I would otherwise have been if it really held my hand in going from the notes to exercises.

In general, it's hard to really know what to complain about with this book because it really doesn't do anything wrong other than just being really dry/boring at times.

[Sebastian S]

not gonna claim to have read the *whole* thing, I suppose one day I will have, probably like 75%. When I was a teenager and heard the word topology I instantly knew i liked whatever it meant. This was said to be the classic way. Indeed, many years later, not only was I instructed using this book, I was also caught off guard as to how lucid, considered, and well presented it was.

[Michael Yu]

It is clear and really good introduction to the subject. I take one month to finish it after my advanced Calculus class but still learn a lot from the book. It is an example of text book for self-study.

[Sam]

I enjoy the writing of this book and the examples. In particular, I think the section on coverings and fundamental group to be quite good as a reference (or to learn about for the first time). The section on the separability axioms and Urysohn's Lemma is also very well presented.

[Hmys]

I only read the first 4 chapters and the first three chapters on algebraic topology. I found those extremely easy to read. I don't know if this is because Munkres is an especially great textbook, or because the material is just naturally easy, but I certainly didn't see any flaws in the book.

[Pingus Conrad]

A fine first pass with the topic, although it has a heavy focus on abstract spaces and their pathologies, which is not really necessary for most undergraduates. At least, it is an excellent reference text.

[Fatima]

This was really great and clear. The classic textbook that introduces the reader to the subject. It spends a lot of time on Set theory at the beginning and goes really slow but I think it's important not to skip the fundamentals when you're starting out

[Oneofmyweirdaccounts]

it's not so bad, i judt hate topology a lot. This boom pretends to be a nice introduction book, but it is almost impossible to understand without a teacher or some online topology lectures

[Jackson Michalak]

Truly an incredible book for an incredible topic

[Thomas Bell]

Great book. Very clear proofs and examples. Everyone who studies math should eventually go through this book.

[Balgivind]

good

[Hassan Zayour]

I think this is one the best undergrad math books I've worked with; very concise, elegant proofs, nice problems, etc...
I still have some of the final chapters to cover in the winter.

[Lin]

Probably one of the best books for a first course in Topology for math undergrads

[NoName66]

A really good book, finished point set topology and some topics of fundamental groups.