论文标题
有限度量和$ k $ - 超级空间上的底座
Finite metric and $k$-metric bases on ultrametric spaces
论文作者
论文摘要
给定一个公制空间$（x，d）$，如果$ x $的$ k $ - \ emph {metric generator}称为$ k $ s $ x $，则为$ x $，如果$ x $的任何一对$ x $的不同点至少由$ s $ $ s $的$ k $元素区分。 a $ k $ - \ emph {metric basis}是$ x $中最低基数的$ k $的生成器。我们证明，超规模空间没有$ k> 2 $的有限$ k $ - 底座。我们还表征了超规模空间的度量和2米基础何时有限，并且在有限的情况下，我们将其表征它们。最后，我们证明只有知道指标基础和其中点的坐标，就可以轻松地恢复超规模空间。
Given a metric space $(X,d)$, a set $S\subseteq X$ is called a $k$-\emph{metric generator} for $X$ if any pair of different points of $X$ is distinguished by at least $k$ elements of $S$. A $k$-\emph{metric basis} is a $k$-metric generator of the minimum cardinality in $X$. We prove that ultrametric spaces do not have finite $k$-metric bases for $k>2$. We also characterize when the metric and 2-metric bases of an ultrametric space are finite and, when they are finite, we characterize them. Finally, we prove that an ultrametric space can be easily recovered knowing only the metric basis and the coordinates of the points in it.
