Sign in to follow this  

Books on Topology?

This topic is 4684 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Hi all, I have been interested in the study of topology for a while know, after spending some time with set theory and some (basic) real anylisis. I have looked around a bit, but I can't seem to find any textbook that would give me a real good overview to the subject. Is there such a standard book? I have read some of the Wiki's entries on topology, but at the moment that's all I seem to be able to come up with. Thanks neo88

Share this post


Link to post
Share on other sites
Armstrong's Basis Topology is a great introduction. It starts off with an overview of point-set topology which is good for anyone who has a background in real analysis. Then it goes into some algebraic topology (fundamental groups and an introduction to simplicial homology). It ends with some pretty cool theorems like the classification of orientable 2-manifolds.

Share this post


Link to post
Share on other sites
I'd recommend Sutherland, Introduction to Metric and Topological Spaces, although it is the purest, most abstract kind of topology and that may not be what you're looking for. It's presented well and in full depth without being long winded.

From your background in Set Theory and Real Analysis it's the best way forward.

Although if you're looking for more to do with manifolds etc it's no use. But then manifolds actually aren't very interesting before you get to knot theory, at least not after the initial interest.

Share this post


Link to post
Share on other sites
I don't have much experience with topology. Just a single one semester course on the subject. The text we used was Armstrong's Basic Topology which was mentioned before. It's a dry read and relatively concise, but is definitely a good text. I'd recommend it.

As for what you need to begin learning topology, I forget what the course prereq's were. However, I hadn't taken analysis yet, nor had I studied set theory in depth. I'd say if you know how to think mathematically and know the basics about sets (what they are, how to perform intersections, unions, and take the compliment) you'd be in a decent place to start reading Basic Topology.

Share this post


Link to post
Share on other sites
Quote:
Original post by Khaos Dragon
Are set theory and real analysis the major tenets required to begin learning topology?


Maybe not the major tenets, but it's good to know. Some more advanced discrete math (like relations, posets, recurrence relations, equivelance relations, graph theory) also helps, in the sense that the mathematical literacy will help you understand.

And note, texts on Topology tend to be dense. I mean dense. Just take it one step at a time; start at chapter one and don't progress unless you've gotten it. It's not too difficult, but it requires some patience for mathematical formality; any background in formal mathematics(axioms, theorems, etc) will help a lot; real analysis should do.

Share this post


Link to post
Share on other sites
No you don't need to know set theory or analysis to understand those introductory books (Hatcher, the first one mentioned, does assume basic analysis and topology).

To learn algebraic topology, it's useful to know a bit of group theory.

Math books in general aren't exactly page-turners, but they're rewarding if you put in the effort. I'd disagree with the above strategy of trying to understand everything before you move on. That'll take forever, and it's sometimes better to read ahead to motivate stuff that is covered earlier.

Share this post


Link to post
Share on other sites
You might be better served with a book on differential topology as opposed to general topology. I'm just guessing that because the former lends itself more readily to computation than the latter, so it is more relevant to computer science and especially 3-D concepts.

Share this post


Link to post
Share on other sites
Guest Anonymous Poster
I wanted to get a grasp for general topology first, as I have not yet taken a course in differental equations. Right now, this is just a little hobby for me, as I'm not really going to be using any of the topological concepts at the momment.
Thanks for that book list it is very helpful!

neo88

Share this post


Link to post
Share on other sites

This topic is 4684 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this