Open Access
1997/1998 A Note on Cantor Sets
Eduardo J. Dubuc
Author Affiliations +
Real Anal. Exchange 23(2): 767-772 (1997/1998).


The Cantor set is constructed by the iterate deletion of a middle interval equidistant from the end points. It is well known that the sums of points in the set cover completely the real line. It was an open problem to know if this property was still true for the sets obtained when the deleted interval is not any more equidistant from the end points. In this note we answer this question positively. We give a simple proof that reflects the geometric nature of the problem, and that is a variation on an old idea that goes back to Steinhaus.


Download Citation

Eduardo J. Dubuc. "A Note on Cantor Sets." Real Anal. Exchange 23 (2) 767 - 772, 1997/1998.


Published: 1997/1998
First available in Project Euclid: 14 May 2012

zbMATH: 0943.26003
MathSciNet: MR1639965

Primary: 26A03
Secondary: 54F50

Keywords: {Cantor ternary set}

Rights: Copyright © 1999 Michigan State University Press

Vol.23 • No. 2 • 1997/1998
Back to Top