On conditionally convergent series

Анотація

The most interesting result of the paper is that for any two complemen- tary subsets A and B of the set of positive odd integers there exists such a sequence {a_k}^∞_k=1 Ì [-1,1] that
"mÎ A:the series is convergent and
"mÎ B:the series is divergent.
Using the map as a substitute of the power function, one can prove similar results for vectors and positive not necessarily integer exponents l.