There are no$C$^{1}-stable intersections of regular Cantor sets

Carlos Gustavo Moreira Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110

Algebraic Topology and General Topology 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 $ .
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@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.
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