Recommended Set Theory Textbooks for Studying Topology and Beyond

[kostas230]

I'm a physics undergraduate and I'll starting learning topology from Munkres next semester. But first I want to learn set theory to feel more comfortable. Do you know any good textbook? A friend of mne from the math department said I should go with Kaplansky's "Set Theory and Metric Spaces".

 

[micromass]

You don't really need to go through a set theory book. Munkres is self-contained and introduces everything you need. Apart from the standard set theoretical operations, you won't need much set theory? So you need to know very well things like

$$A\subseteq f^{-1}(f(A))$$

but not much more.

Anyway, Kaplansky is a decent book. My favorite book on set theory is Hrbacek and Jech. This book has the benefits of starting from the axioms of set theory and to build up everything from that.

 

[mathwonk]

Other references include: the standard in the old days was Halmos's Naive set theory. I liked Erich Kamke's book too.

http://www.abebooks.com/servlet/Sea...&sortby=17&sts=t&tn=naive+set+theory&x=67&y=7

http://www.abebooks.com/servlet/SearchResults?an=erich+kamke&kn=set+theory

The classic is the one by Hausdorff:

http://www.abebooks.com/servlet/Sea...d=all&sortby=17&sts=t&tn=set+theory&x=62&y=10

If you want to see what "the man" himself said, for historical interest, although not necessarily recommended as a place to learn easily, there is always Georg Cantor's own work:

http://www.abebooks.com/servlet/SearchResults?an=georg+cantor&sts=t&tn=transfinite+numbers

 

[Sankaku]

Halmos is great. I found a nice inexpensive paperback reprint a little while back.

He writes so well...

 

[kostas230]

You don't really need to go through a set theory book. Munkres is self-contained and introduces everything you need. Apart from the standard set theoretical operations, you won't need much set theory? So you need to know very well things like

A⊆f−1(f(A))

I'd like to have a good knowledge of set theory before I start learning topology, because it would make me feel much more comfortable knowing the fundamentals. Also, I suppose I will need set theory for further studies in algebra and topology.

Other references include: the standard in the old days was Halmos's Naive set theory. I liked Erich Kamke's book too.

I think I will go with Halmo's book. Thanks mathwonk!