Some Existence Results on Cantor Sets

Published 8 Mar 2016 in math.GM | (1603.05121v3)

Abstract: 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.

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