Real Analysis Exchange

Avoiding Rational Distances

Ashutosh Kumar

Full-text: Open access

Abstract

We show that for any set of reals \(X\) there is a \(Y \subseteq X\) such \(X\) and \(Y\) have same Lebesgue outer measure and the distance between any two distinct points in \(Y\) is irrational.

Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 493-498.

Dates
First available in Project Euclid: 27 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894908

Mathematical Reviews number (MathSciNet)
MR3261893

Zentralblatt MATH identifier
1295.32020

Subjects
Primary: 03E75: Applications of set theory

Keywords
outer measure forcing

Citation

Kumar, Ashutosh. Avoiding Rational Distances. Real Anal. Exchange 38 (2012), no. 2, 493--498. https://projecteuclid.org/euclid.rae/1403894908


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