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In article
<12708828.1122723804279.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Xantos <xantos_2005@xxxxxxxxx> wrote:
> 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
If a series of reals converges, then all but countably many are zero.
Series with some other values (say a topological vector space) need not
have this property.
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