论文标题
一般而言，毒液套件是Cantor套装
Diophantine sets in general are Cantor 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 |。 $$在本文中，我们研究了这些集合的拓扑结构，我们表明，对于大$τ$，几乎所有$γ> 0 $，$ d_ {γ，τ} $是cantor套装。
Let $γ\in(0;\frac{1}{2}),τ\geq 1$ and define the "$γ,τ$ Diophantine set" as: $$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|. $$ In this paper we study the topology of these sets and we show that, for large $τ$ and for almost all $γ>0$, $D_{γ,τ}$ is a Cantor set.
