The topological structure of the set of \(P\)-sums of a sequence. II (Q2707256)

Let \(\lambda _n\) be a sequence of reals such that \(\sum |\lambda _n |<\infty \), \(P\) a finite set of reals and let \(S\) consist of all the sums of the form \(\sum \varepsilon _n\lambda _n\), where \(\varepsilon _n\in P\). The structure of \(S\) is described up to homomorphism, provided that \(P\) is symmetric and \(\lambda _n\) satisfies a certain lacunarity condition. This extends results of \textit{J. A. Guthrie} and \textit{J. E. Nymann} [Colloq. Math. 55, 323-327 (1988; Zbl 0719.40004)] and the authors [Publ. Math. 50, 305-316 (1997; Zbl 0880.11013)].