Is the concept of conditional convergence of series whose terms are real numbers a topic of research in analysis or merely something to be aware of?

The question is prompted by the conjunction of my participation in some mathoverflow threads about rearrangements of series and the fact that I've started writing something about how a simple trigonometry problem led to a question whose answer is independent of the usual axioms of set theory.

I find myself thinking of things like this: For each conditionally convergent series there is a set of permutations of the indices that do not alter the sum, and there is a function from the set of rearrangements to the set of sums, and for each permutation of the indices there is a set of series whose sums it does not alter, and for each such permutation there is a mapping from sums to changes worked by that permutation, and there could be theorems about these objects. BUT is there some point to doing any of this?