论文标题
在欧几里德空间中固定半径的开放球的互动中
On the complements of union of open balls of fixed radius in the Euclidean space
论文作者
论文摘要
让$ r $ - body成为$ \ mathbb {e}^d $的RADIUS $ r $ r $的敞开球的补充。 $ r $ $ hulloid的封闭式非空套$ a $，最小$ r $ - 包含$ a $的体；如果$ a $是单纯形的顶点，则完全描述了$ a $的$ r $ hulloid（如果$ d = 2 $），如果$ d> 2 $> 2 $进行了特殊示例。如果$ d = 2 $，则$ r $ $ bodies的类是紧凑的，但如果$ d> 2 $，则不紧凑。
Let an $R$-body be the complement of the union of open balls of radius $R$ in $\mathbb{E}^d$. The $R$-hulloid of a closed not empty set $A$, the minimal $R$-body containing $A$, is investigated; if $A$ is the set of the vertices of a simplex, the $R$-hulloid of $A$ is completely described (if $d=2$) and if $d> 2$ special examples are studied. The class of $R$-bodies is compact in the Hausdorff metric if $d =2$, but not compact if $d>2$.
