Avoiding rational distances

Seminar
Speaker
Ashutosh Kumar (HUJI)
Date
16/11/2014 - 10:15Add to Calendar 2014-11-16 10:15:00 2014-11-16 10:15:00 Avoiding rational distances Komjath has asked the following question: Let X be a subset of Euclidean space. Must there exist a subset Y of X such that X and Y have same outer measure and the distance between any two points in Y is irrational?    We'll show that this is true in dimension one. Our proof relies on some work of Gitik and Shelah on forcings with sigma ideals.   Bibliography אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

Komjath has asked the following question: Let X be a subset of Euclidean space. Must there exist a subset Y of X such that X and Y have same outer measure and the distance between any two points in Y is irrational? 

 
We'll show that this is true in dimension one. Our proof relies on some work of Gitik and Shelah on forcings with sigma ideals.
 

Last Updated Date : 12/11/2014