$\hat{I}´$-Badly approximable numbers and ubiquitously losing sets

Jimmy Tseng

We consider a natural filtration $\mathrm{Bad}(\hat{I}´)\subset \mathrm{Bad}(\hat{I}{´}^{\prime })$ for $\hat{I}´\ge \hat{I}{´}^{\prime }>0$ on the set of badly approximable numbers to c…