On the descriptive complexity of Salem sets
On the descriptive complexity of Salem sets
In this paper we study the notion of Salem set from the point of view of descriptive set theory. We first work in the hyperspace $\mathbf{K}([0,1])$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbolΠ^0_3$-complete family. This is done by characterizing the complexity of …