Author

Mumtaz Hussain

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Preprint Aug 2026

Well and badly approximable sets, and rapid winning

The set of $\tau$-approximable numbers, $\mathcal W(\tau)$, has genuinely fractional Hausdorff dimension, whereas the set of inhomogeneously badly approximable numbers, $\Bad^\gamma$, has full Hausdorff dimension. We determine the Hausdorff dimension of their intersection by introducing the $\Psi$-rapid game, a scale-s...

Mumtaz Hussain, David Simmons · 1 citation · ⚡1