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 · 981 ratings  · 36 reviews
Start your review of Topology
Matthieu
Sep 25, 2009 rated it it was amazing
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

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.

...more
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Overrated and outdated.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 los

Overrated and outdated.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.

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Pietro
Sep 04, 2007 rated it it was amazing
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. 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. ...more
Júlio
May 04, 2021 rated it really liked it
Good introduction to General Topology (which was the part of the book I really read.)
Matthew Zabka
Mar 18, 2018 rated it it was amazing
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
Jul 22, 2020 rated it it was amazing
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.
Michael Yu
Sep 15, 2018 rated it it was amazing
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. 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. ...more
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 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 ...more
Jackson Michalak
Truly an incredible book for an incredible topic
Thomas Bell
Jun 10, 2019 rated it it was amazing
Great book. Very clear proofs and examples. Everyone who studies math should eventually go through this book.
H.A.A. Zayour
Dec 02, 2020 rated it it was amazing
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.
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.
...more
Lin
Jan 08, 2021 rated it it was amazing
Probably one of the best books for a first course in Topology for math undergrads
Lolololl
munkres is like popsci but for mathematicians
Ian Paredes
Mar 03, 2008 rated it really liked it
rough book to get through and it doesn't motivate the concepts of a topological space right away from metric spaces, but this is a minor oversight and doesn't really detract from the book's strengths. i haven't read this book in a while so i can't really give a detailed account about it's strengths and weaknesses, but there's a reason why it's a standard text in most universities here in the united states. i recommend the reader to supplement this text with mendelson's topology text, which i bel rough book to get through and it doesn't motivate the concepts of a topological space right away from metric spaces, but this is a minor oversight and doesn't really detract from the book's strengths. i haven't read this book in a while so i can't really give a detailed account about it's strengths and weaknesses, but there's a reason why it's a standard text in most universities here in the united states. i recommend the reader to supplement this text with mendelson's topology text, which i believe is published by dover; his text motivates the ideas from metric spaces, which i believe is a better approach when dealing with an audience who have never even dealt with any notion of topological neighborhoods outside of, say, introductory real analysis. ...more
Ming
Jan 10, 2015 rated it really liked it
Finished the 1st half of the book (i.e. the stuff before Chapter 40). Munkres is pretty lucidly written for the most part, contains somewhat interesting exercises. Not too keen about how countability axioms were introduced (e.g. how do you demonstrate something possesses a countable basis? You need to demonstrate that this countable basis generates a topology that is finer than the topology that the set currently possesses. This is not made clear. Also, his decision to refer to it as a "basis" i Finished the 1st half of the book (i.e. the stuff before Chapter 40). Munkres is pretty lucidly written for the most part, contains somewhat interesting exercises. Not too keen about how countability axioms were introduced (e.g. how do you demonstrate something possesses a countable basis? You need to demonstrate that this countable basis generates a topology that is finer than the topology that the set currently possesses. This is not made clear. Also, his decision to refer to it as a "basis" instead of "base", which is the terminology most other txtbooks use.) But still, it is accessible, and pretty enjoyable. ...more
Dan
Mar 19, 2008 rated it it was amazing
I think this might be the best math text book ever written.

I learned Topology from this book. This book is THE text to learn topology from. This book is a rare combination in that it teaches the material very well and it can be used as a reference later.

The treatment on algebraic topology later in the book is a little light.

Geoffrey Lee
Dec 17, 2008 rated it really liked it
This book contains a great introduction to topology (more point-set than algebraic). I must admit, I have not read all of the first part of the book, but Munkres certainly makes it easier for a beginner to accept and understand the seemingly over-abstract definitions involved in point-set topology.
Chris Curtis
Nov 14, 2008 rated it it was amazing
If you need to learn point-set topology this is the place to do it. I can't vouch for all of the AT material in the latter half, but I imagine it is as good as the rest of the book. If only all texts were this clear. If you need to learn point-set topology this is the place to do it. I can't vouch for all of the AT material in the latter half, but I imagine it is as good as the rest of the book. If only all texts were this clear. ...more
Ronald Lett
Dec 26, 2011 rated it liked it
Recommends it for: Mathematics majors
An excellent introduction to point-set and light algebraic topology. If this is your first exposure to topology, I would recommend Kinsey's "Topology of Surfaces" as a companion of solid applications in the specific case of compact 2-dimensional topology. An excellent introduction to point-set and light algebraic topology. If this is your first exposure to topology, I would recommend Kinsey's "Topology of Surfaces" as a companion of solid applications in the specific case of compact 2-dimensional topology. ...more
Nigel Lim
Dec 16, 2016 rated it it was amazing
Delightfully clear exposition and rigorous proofs. The exercises vary from simple applications of theorems to challenging proofs. Good, clean treatment of point-set topology and algebraic topology (the latter is somewhat light, often confined particularly to results on 2-dimensional spaces).
Mohit Jindal
Evan
Oct 18, 2010 rated it liked it
Among the best mathematical texts I've ever read... really, fun to read. Among the best mathematical texts I've ever read... really, fun to read. ...more
Chrish
Ojas
Oct 24, 2007 rated it liked it
nice book on topology, challenging problems, but text is too wordy
Anand Gopal
Apr 05, 2017 rated it really liked it
I enjoyed this introduction to mathematical topology. It manages to provide clear explanations with examples, without sacrificing rigor.
Joe Cole
Apr 13, 2017 rated it it was amazing
The text is generally pleasant to read. The proofs are well structured and complete. This is especially true for results central to the theory. I found most of the explanations very well worded and easy to follow

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