Real Analysis Exchange

A Note on Cantor Sets

Eduardo J. Dubuc

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Abstract

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

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

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337001382

Mathematical Reviews number (MathSciNet)
MR1639965

Zentralblatt MATH identifier
0943.26003

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

Keywords
{Cantor ternary set}

Citation

Dubuc, Eduardo J. A Note on Cantor Sets. Real Anal. Exchange 23 (1999), no. 2, 767--772. https://projecteuclid.org/euclid.rae/1337001382


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