ALGEBRAIC AND TOPOLOGICAL PROPERTIES OF SOME SETS IN l1

For a sequence x is an element of l(1) / c(00), one can consider the set E (x) of all subsums of the series Sigma(infinity)(n=1) x(n). Guthrie and Nymann proved that E(x) is one of the following types of sets: (I) a finite union of closed intervals; (C) homeomorphic to the Cantor set; (MC) homeomorphic to the set T of subsums of Sigma(infinity)(n=1) b(n) where b (2 n - 1) = 3/4(n) and b(2n) = 2/4(n). Denote by I, C and M C the sets of all sequences x is an element of l(1) / c(00) such that E(x) has the property (I), (C) and (MC), respectively. We show that I and C are strongly c-algebrable and MC is c-lineable. We also show that C is a dense G(delta)-set in l(1) and I is a true F-sigma-set. Finally we show that I is spaceable while C is not.