# MathSciDoc: An Archive for Mathematician ∫

#### mathscidoc:1701.02001

Acta Mathematica, 206, (2), 311-323, 2009.4
We prove that there are no stable intersections of regular Cantor sets in the$C$^{1}topology: given any pair ($K$,$K$′) of regular Cantor sets, we can find, arbitrarily close to it in the$C$^{1}topology, pairs $\left( {\tilde{K},\tilde{K}'} \right)$ of regular Cantor sets with $\tilde{K} \cap \tilde{K}' = \emptyset$ .
@inproceedings{carlos2009there,
title={There are no$C$^{1}-stable intersections of regular Cantor sets},
author={Carlos Gustavo Moreira},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203356682488740},
booktitle={Acta Mathematica},
volume={206},
number={2},
pages={311-323},
year={2009},
}

Carlos Gustavo Moreira. There are no$C$^{1}-stable intersections of regular Cantor sets. 2009. Vol. 206. In Acta Mathematica. pp.311-323. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203356682488740.