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<sub>n</sub> (x<sub>n</sub>) that is, sets of sequences x = (x<sub>n</sub>) for which the series converges, or has a sum (perhaps infinite), or oscillates. Provided all ƒ<sub>n</sub> are continuous real functions, sufficient conditions are given for the “convergence” sets to be of the first Baire category or residual in s.
