The structure of the fréchet space s regarding the series ∑ƒ_n(x_n)

We investigate the subsets of the Fr´echet space s of all sequences of real numbers equipped with the Fr´echet metric ρ from the Baire category point of view. In particular, we concentrate on the “convergence” sets of the series ∑ƒ_n (x_n) that is, sets of sequences x = (x_n) for which the series converges, or has a sum (perhaps infinite), or oscillates. Provided all ƒ_n are continuous real functions, sufficient conditions are given for the “convergence” sets to be of the first Baire category or residual in s.