Real Analysis Exchange

A Note on Cantor Sets

Eduardo J. Dubuc

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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.

Article information

Real Anal. Exchange, Volume 23, Number 2 (1999), 767-772.

First available in Project Euclid: 14 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A03: Foundations: limits and generalizations, elementary topology of the line
Secondary: 54F50: Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]

{Cantor ternary set}


Dubuc, Eduardo J. A Note on Cantor Sets. Real Anal. Exchange 23 (1999), no. 2, 767--772.

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