2 problems

Let a Borel subgroup or Borel subring of the reals mean a subgroup or subring of $\mathbb{R}$ that is Borel as a subset, and let Hausdorff dimension refer to its dimension as a sub…

Let $\mathcal{K}$ be a separable Rosenthal compact, let $\mathbb{N}$ denote the set of natural numbers, and let $D$ be a countable dense subset of $\mathcal{K}$. Write…