Looking for a topology textbook

Can anyone suggest a good topology textbook for self-study? Are there any prerequisites I should know first? (For example, do I need to study set theory first?)


The best general topology book I know of is General Topology by Stephen Willard; I believe it’s out of print, however. A couple of others I’m familiar with are Elementary Topology by Michael Gemignani (which could make a great choice, since it’s paperback and cheap, and possible the most accessible of these three), and Topology: A First Course by James Munkres, either of which would also be a good introduction. I don’t know what kind of background you have, but either of these should be accessible for someone who’s had some higher undergraduate level math (such as abstract algebra or analysis). Look 'em up on Amazon for more opinions.

Topology isn’t too far removed from set theory, so you do need to have a basic, working knowledge of set theory. All three of these books do have a first chapter covering some of the basics of set theory. Let me know if you have any more questions about the books.

I’ve taken calculus up to the level of linear algebra, and via QM have some experience with differential equations. I’ve also studied number theory and some group theory on my own. Does that help?


Yeah, that does help. The main reason I mentioned your math background was that I was wondering how much experience you have reading higher math texts in general. If you’ve self-studied number theory and group theory, I’m sure you’re familiar with the “dense” writing in those types of texts. Other than that familiarity, you really don’t need much of a math background in any specific area to learn topology, calculus is helpful, since topology grew out of attempts to generalize ideas such as continuity and convergence, and knowing that can help put things in some perspective.

You really don’t need to know much set theory, with your background, I’m sure you’re familiar enough with the basics to learn topology; anything you’re not familiar with would be introduced within the book. Anyway, with all that said, my recommendation would be Elementary Topology by Gemignani that I mentioned above, mainly 'cause it’s cheap (under $10 on Amazon), and not a bad book at all.

Good luck!

Thanks! This is a real relief. I’ll look for the books you suggested in the library, and use Amazon if all else fails.

(So many subjects, so little time…)


I found Set Theory and Metric Spaces by Irving Kaplansky eminently readable, although it’s not strictly a topology text. Even though it may be somewhat off topic from what you were looking for, Ben, it is so beautifully written that I think you’d like it regardless.

Cabbage, do you know this little gem of a book, or know Irving Kaplansky? (He was Canadian, you know).

The name Kaplansky seems to ring a bell somewhere back in my mind, but I’m not really familiar with him or with the book. It does sound like something worth checking out, I should have mentioned earlier that familiarity with metric spaces would definitely make learning topology easier.

At a slight tangent to your OP, I’m almost certain you will also enjoy “Curious and Interesting Geometry” by David Wells. It might provide some excellent ‘recreational’ reading while you get stuck into all those textbooks! It covers many fascinating aspects of topology as well as other, related areas.