Generalized series

[Xantos]

Hello,


Nets are generalized sequences. In the same manner
series can be generalized. I don't know it they also
have some fancy name. 

If the generalized series Sum_i(x_i) converges,
then it is easy to show that the net 
(x_i) is a zero-net.

But what I really would like to know is whether
in that case at most countably many x_i's are different from zero. That is to 
say, the summation can be 
done only on countable subset of I. 
Thank you for your comments.

Xantos