How much Set Theory before Topology? I was reading Baby Rudin for Real Analysis and wanted to explore Topology a little deeper. I bought George Simmons' Introduction to Topology and Modern Analysis and found myself liking it. I am having some problems every once in a while with prerequisites.
How much Set theory do I need to learn before diving into the aforementioned book?
Also, the book is divided into 3 parts : Topology, Operators and Algebras of Operators. 
Till where can I trot with a good understanding of SV Calculus?
 A: Simmons' book has a brief introduction to set theory at the beginning. If you can get through it without any trouble, you probably have a strong enough background in set theory. In the worst case, there may be a couple of things that you will get stuck at. If that happens, you can go try to figure it out on your own, and if that fails go back to a reference for set theory. This should be pretty infrequent.
The best thing to do is to try to read the book (and understand every line of every proof, not just skimming over it). If you get stuck, find a way to get past it. If you find yourself frequently getting stuck, figure out what it is you're weak on, and go study that before you go back to the book.
A: I assume that in the book you are asking about the preliminaries included by author would be sufficient.
One thing which I consider useful is Zorn's lemma, which is in the first chapter of Simmons' book. But even if you choose different text, you will bump into using Zorn's lemma a few times.
Other than that, the only thing that I can think of are ordinals and transfinite induction. But they are perhaps less important. Many of the books that are intended as the first course in general topology don't include them. (For instance, Willard includes these two topics.)
However, I don't think you should worry too much about preliminaries. You can always get back to some topic, if you find at some point in the book, that you need to know something from set theory (or any other area).
