${\bf Bad}(s,t)$ is hyperplane absolute winning
Volume 164 / 2014
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.
