Winning Sets, Quasiconformal Maps and Diophantine Approximation

This paper describes two new types of winning sets in mathbbRⁿ{mathbb{R}^n}, defined using variants of Schmidt’s game. These strong and absolute winning sets include many Diophantine sets of measure zero and first category, and have good behavior under countable intersections. Most notably, they are invariant under quasiconformal maps, while classical winning sets are not.