A Technique of Studying Sums of Central Cantor Sets

http://dx.doi.org/10.4153/CMB-2001-002-8
Canad. Math. Bull. 44(2001), 12-18

  Published:2001-03-01
 Printed: Mar 2001

This paper is concerned with the structure of the arithmetic sum of a finite number of central Cantor sets. The technique used to study this consists of a duality between central Cantor sets and sets of subsums of certain infinite series. One consequence is that the sum of a finite number of central Cantor sets is one of the following: a finite union of closed intervals, homeomorphic to the Cantor ternary set or an $M$-Cantorval.