We investigate the subsets of the Fr\'echet space $s$ of all sequences of real numbers equipped with the Fr\'echet metric $\rho$ from the Baire categorypoint of view. In particular, we concentrate on the "convergence" sets of the series $\sum f_n \left(x_n\right)$ that is, sets of sequences $x=(x_n)$for which the series converges, or has a sum (perhaps infinite), oroscillates. Provided all $f_n$ are continuous real functions, sufficientconditions are given for the "convergence" sets to be of the first Bairecategory or residual in $s$.
@article{40,
title = {The structure of the Fr\'echet space $s$ regarding the series $\sum f\_n\left(x\_n\right)$},
journal = {Tatra Mountains Mathematical Publications},
volume = {43},
year = {2009},
doi = {10.2478/tatra.v44i0.40},
language = {EN},
url = {http://dml.mathdoc.fr/item/40}
}
Šalát, Tibor; Vadovič, Peter. The structure of the Fr\'echet space $s$ regarding the series $\sum f_n\left(x_n\right)$. Tatra Mountains Mathematical Publications, Tome 43 (2009) . doi : 10.2478/tatra.v44i0.40. http://gdmltest.u-ga.fr/item/40/