Does anyone know a very good introductory book to topology?

by rayman123
Tags: book, introductory, topology
rayman123 is offline
Nov6-10, 07:18 AM
P: 152
Does anyone know a very good introductory book to topology? I am looking for an introductory book with solved examples, proves and so on.
Phys.Org News Partner Science news on
Scientists pinpoint when harmless bacteria became flesh-eating monsters
Asian air pollution affect Pacific Ocean storms
Rocket leak delays space station delivery launch (Update)
mathwonk is offline
Nov7-10, 07:19 PM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,421
a lot of people like munkres.
rayman123 is offline
Nov8-10, 02:31 AM
P: 152
I will check out this book:) Thank you

jbunniii is online now
Nov10-10, 03:50 PM
Sci Advisor
HW Helper
PF Gold
jbunniii's Avatar
P: 2,890

Does anyone know a very good introductory book to topology?

Munkres is very nice. A good and very cheap alternative ($8.18 at Amazon) is Bert Mendelson's "Introduction to Topology." It doesn't do much, if any, algebraic topology, but its treatment of metric spaces and point-set topology is very clear and well-motivated.
rayman123 is offline
Nov11-10, 03:26 AM
P: 152
ah nice. Many people claim Munkers to be the best topology book, it is going to be interesting to learn from this book. My plan is to improve my mathematical skills as much as possible because I would like to work in the future with mathematical physics and I know that topology and differential geometry are definitely required in order to be able to continue with more advanced mathematical methods;)
micromass is online now
Nov15-10, 01:09 PM
micromass's Avatar
P: 16,506
Munkres is nice. I would recommend Willards 'General topology" tho.

The best is actually to get 2-3 books and read through them simultanuously. It gives different opinions on some matters and it could be quite enlightning...
MathematicalPhysicist is offline
Nov15-10, 01:39 PM
P: 3,169
To add to this, you should also get the book called "counterexamples in topology".

It's a disorganized book, but it has plenty of examples, a terrific companion.
rayman123 is offline
Nov18-10, 08:27 AM
P: 152
thank you! I have ordered this one as well;)
''Mathematical Physicist'' could you please describe more detailed your work (studies) how does it look like to work with this branch of physics? What are perspectives?
Landau is offline
Nov18-10, 12:25 PM
Sci Advisor
P: 905
Munkres is not really my favorite, but it's ok and contains a lot.

Willard, Dugundji, and Kelley are very good books on point-set topology. (I'm assuming you are not talking about algebraic topology.)
radou is offline
Nov18-10, 12:29 PM
HW Helper
radou's Avatar
P: 3,225
Munkres is great, although I don't have any experience with other books in topology.

The exercises are the most valuable part of the book, I think they help you learn a lot.

It is well written, with a lot of comments on the concept of the material. Not only mindless strolling through definitions, theorems, lemmas and proofs. So it can be used for an introductory level.

It has a nice and detailed introductory part dealing with the foundations of mathematics, too, i.e. the prerequisites you need to know.
micromass is online now
Nov18-10, 12:38 PM
micromass's Avatar
P: 16,506
The only thing that I don't like about Munkres are that he doesn't talk about initial/final structures. He also doesn't talk about filters, which is a shame imho, since these concepts have a lot of use outside topology...
But I do like that he talks about point-set and algebraic topology. So you can feel for yourself which part is more fun

Register to reply

Related Discussions
What's the difference between differential topology and algebraic topology? Differential Geometry 5
Standard topology and discrete topology Calculus & Beyond Homework 2
K topology strictly finer than standard topology Calculus & Beyond Homework 5
euclidian topology ang cofinite topology Differential Geometry 5
Topology: Indiscrete/Discrete Topology Calculus & Beyond Homework 1