Isolated points of Diophantine sets

Fernando Argentieri

Let $\gamma \in (0;\frac{1}{2}),\tau \ge 1$ and define the "$\gamma ,\tau$ Diophantine set" as: $$D_{γ, τ}:=\{α\in (0;1): ||qα||\geq\fracγ{q^τ}\quad\forall q\in\Bbb{N}\},\qquad ||x||:=\inf_{p\in\Bbb{…