论文标题
二聚体套件的孤立点
Isolated points of Diophantine sets
论文作者
论文摘要
令$γ\ in（0; \ frac {1} {2}），τ\ geq 1 $ $，并定义“ $γ，τ$ diophantine set” as：$ d_ d_ d_ {γ{γ，τ}：= \ \ \ {α\ in（0; 1）：| qa） q \ in \ bbb {n} \}，\ qquad || x ||：= \ inf_ {p \ in \ bbb {z}} | x-p |。$ $$我们分析了这些集合的拓扑，我们表明它们通常具有孤立的点。
Let $γ\in(0;\frac{1}{2}),τ\geq 1$ and define the "$γ,τ$ Diophantine set" as: $$D_{γ, τ}:=\{α\in (0;1): ||qα||\geq\fracγ{q^τ}\quad\forall q\in\Bbb{N}\},\qquad ||x||:=\inf_{p\in\Bbb{Z}}|x-p|.$$ We analyze the topology of these sets and we show that generally they have isolated points.
