The Achievement Set of Generalized Multigeometric Sequences.

We study the topology of all possible subsums of the generalized multigeometric series k 1 f (x) + k 2 f (x) + ⋯ + k m f (x) + ⋯ + k 1 f (x n) + ⋯ + k m f (x n) + ⋯ , where k 1 , k 2 , ⋯ , k m are fixed positive real numbers and f runs along a certain class of non-negative functions on the unit interval. We detect particular regions of this interval for which this achievement set is, respectively, a compact interval, a Cantor set and a Cantorval. [ABSTRACT FROM AUTHOR]