The Center of Distances of Central Cantor Sets

Abstract

The center of distances of central Cantor sets is investigated. Any central Cantor set is an achievement set of exactly one fast convergent sequence (a_n). We show that the center of distances of the central Cantor set is the union of all centers of distances of F_n where F_n is the set of all n-initial subsums of the series sum a_n. Moreover, we give a necessary and sufficient condition for central Cantor sets to have not the minimal possible center of distances.