On the Structure of Arithmetic Sums of Cantor Sets Associated with Series

This paper continues the investigation started in Anisca and Chlebovec (Nonlinearity 22:2127–2140, 2009). We exhibit conditions which imply that the topological structure of the arithmetic sum of two Cantor sets associated with series is either: a Cantor set, a finite union of closed intervals, or three mixed Cantorvals (R, L and M-Cantorval). Our main results extend and generalize a recent result of Pourbarat regarding sums of homogeneous Cantor sets.