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A Technique of Studying Sums of Central Cantor Sets

Published online by Cambridge University Press:  20 November 2018

Razvan Anisca  and
Monica Ilie
Razvan Anisca
Affiliation:
Department of Mathematical Sciences University of Alberta Edmonton, Alberta T6G 2G1
Monica Ilie
Affiliation:
Department of Mathematical Sciences University of Alberta Edmonton, Alberta T6G 2G1
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Abstract

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This paper is concernedwith 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.

Keywords

11B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 1 , 01 March 2001 , pp. 12 - 18
Copyright
Copyright © Canadian Mathematical Society 2001

References

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