English

Some Existence Results on Cantor Sets

General Mathematics 2018-03-29 v3

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.

Cite

@article{arxiv.1603.05121,
  title  = {Some Existence Results on Cantor Sets},
  author = {Borys Álvarez-Samaniego and Wilson P. Álvarez-Samaniego and Jonathan Ortiz-Castro},
  journal= {arXiv preprint arXiv:1603.05121},
  year   = {2018}
}

Comments

11 pages, added some references, definitions and propositions

R2 v1 2026-06-22T13:12:21.236Z