Skip to main content

Research Repository

Advanced Search

Cantor-winning sets and their applications

Badziahin, D.; Harrap, S.

Cantor-winning sets and their applications Thumbnail


D. Badziahin


We introduce and develop a class of Cantor-winning sets that share the same amenable properties as the classical winning sets associated to Schmidt’s (α, β)-game: these include maximal Hausdorff dimension, invariance under countable intersections with other Cantor-winning sets and invariance under bi-Lipschitz homeomorphisms. It is then demonstrated that a wide variety of badly approximable sets appearing naturally in the theory of Diophantine approximation fit nicely into our framework. As applications of this phenomenon we answer several previously open questions, including some related to the Mixed Littlewood conjecture and the ×2,×3 problem.


Badziahin, D., & Harrap, S. (2017). Cantor-winning sets and their applications. Advances in Mathematics, 318, 627-677.

Journal Article Type Article
Acceptance Date Jul 31, 2017
Online Publication Date Aug 28, 2017
Publication Date Aug 28, 2017
Deposit Date Dec 30, 2015
Publicly Available Date Aug 28, 2019
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 318
Pages 627-677
Related Public URLs


You might also like

Downloadable Citations