Some Existence Results on Cantor Sets
  The existence of two different Cantor sets, one of them contained in the set of Liouville numbers and the other one inside the set of Diophantine numbers, is proved. Finally, a necessary and sufficient condition for the existence of a Cantor set contained in a subset of the real line is given. 
Borys \'Alvarez-Samaniego, Wilson P. \'Alvarez-Samaniego and Jonathan   Ortiz-Castro
math.GM