Do community colleges have good mathematics libraries (with advanced books)? I am sure that it is different from place to place. I am interested to get some feeling of the general situation.
Of course, as Dave Clarke says, every institution is different. However, in general I would expect the answer is no.
Community colleges typically offer only lower-division courses and don't expect their students or faculty to carry on research. Moreover, they are usually publicly funded and charge only nominal tuition, so they are not likely to have a lot of extra money. Given this, it's difficult to see why a community college librarian would want to spend money acquiring advanced mathematics books or journals.
That said, a community college library would almost certainly have access to the interlibrary loan network, allowing one to (eventually) acquire any resource of interest. Some might also have a reciprocity agreement with a nearby research university library. It is also quite possible they would have access to online databases that could include a lot of material in mathematics.
I fully agree with Nate Eldredge's answer, but here are some resources for exploring what sorts of mathematics books you might find at primarily undergraduate institutions:
If there are specific community colleges you are thinking of applying to, you can look for an online library catalog, or visit the library in person and check it out. This is by far the most reliable way to tell whether you would be happy with the library.
The Mathematical Association of America provides a basic library list of books recommended for undergraduate libraries, annotated with how essential they feel the book is. Decades ago the list had two-year and four-year sections, but nowadays it is probably aimed more at four-year colleges. Still, it will give an upper bound for what one can reasonably expect of a typical community college. You won't find research monographs on the list.
The American Mathematical Association of Two-Year Colleges apparently had a similar list, at least as of 1993 when these guidelines were written (see D.1), but I cannot find it online. You could probably learn more by asking them.
Of course, underfunded institutions may lack even the most essential books on the basic library list, while fancy schools may have all of them and more. Note that while there are some pretty fancy liberal arts colleges out there, you don't generally run across community colleges with big budgets.