topology

[rayman123]

Does anyone know a very good introductory book to topology? I am looking for an introductory book with solved examples, proves and so on.
Thanks

[mathwonk]

a lot of people like munkres.

[rayman123]

I will check out this book:) Thank you

[jbunniii]

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]

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]

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]

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]

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]

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]

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]

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 :smile: