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${\bf Bad}(s,t)$ is hyperplane absolute winning

Volume 164 / 2014

Erez Nesharim, David Simmons Acta Arithmetica 164 (2014), 145-152 MSC: Primary 11J13. DOI: 10.4064/aa164-2-4

Abstract

J. An proved that for any $s,t \geq 0$ such that $s + t = 1$, $\mathop {\bf Bad}\nolimits (s,t)$ is $(34\sqrt 2)^{-1}$-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that $\mathop {\bf Bad}\nolimits (s,t)$ is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of $\mathop {\bf Bad}\nolimits (s,t)$ intersected with certain fractals.

Authors

  • Erez NesharimSchool of Mathematical Sciences
    Tel Aviv University
    Ramat Aviv
    Tel Aviv 6997801, Israel
    e-mail
  • David SimmonsDepartment of Mathematics
    Ohio State University
    231 W. 18th Avenue
    Columbus, OH 43210-1174, U.S.A.
    e-mail

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