The structure of the Fr\'echet space $s$ regarding the series $\sum f_n\left(x_n\right)$

Year, pages: 2009, 1 - 8

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 category point 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), or oscillates. Provided all $f_n$ are continuous real functions, sufficient conditions are given for the ``convergence" sets to be of the first Baire category or residual in $s$.

Šalát, T., Vadovič, P. 2009. The structure of the Fr\'echet space $s$ regarding the series $\sum f_n\left(x_n\right)$. In Tatra Mountains Mathematical Publications, vol. 44, no.3, pp. 1-8. 1210-3195.

Šalát, T., Vadovič, P. (2009). The structure of the Fr\'echet space $s$ regarding the series $\sum f_n\left(x_n\right)$. Tatra Mountains Mathematical Publications, 44(3), 1-8. 1210-3195.