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Finite Ultrametric Balls
p-Adic Numbers, Ultrametric Analysis and Applications Pub Date : 2019-07-01 , DOI: 10.1134/s2070046619030014 Oleksiy Dovgoshey
p-Adic Numbers, Ultrametric Analysis and Applications Pub Date : 2019-07-01 , DOI: 10.1134/s2070046619030014 Oleksiy Dovgoshey
The necessary and sufficient conditions under which a given family $\mathcal{F}$ of subsets of finite set $X$ coincides with the family $\mathbf B_X$ of all balls generated by some ultrametric $d$ on $X$ are found. It is shown that the representing tree of the ultrametric space $(\mathbf B_{X}, d_H)$ with the Hausdorff distance $d_H$ can be obtained from the representing tree $T_X$ of ultrametric space $(X, d)$ by adding a leaf to every internal vertex of $T_X$.
中文翻译:
有限超测量球
找到了有限集$X$子集的给定族$\mathcal{F}$与由$X$上的一些超度量$d$生成的所有球的族$\mathbf B_X$重合的充分必要条件. 结果表明,从超度量空间$(X, d)$的表示树$T_X$可以得到具有Hausdorff距离$d_H$的超度量空间$(\mathbf B_{X}, d_H)$的表示树通过向 $T_X$ 的每个内部顶点添加一个叶子。
更新日期:2019-07-01
中文翻译:
有限超测量球
找到了有限集$X$子集的给定族$\mathcal{F}$与由$X$上的一些超度量$d$生成的所有球的族$\mathbf B_X$重合的充分必要条件. 结果表明,从超度量空间$(X, d)$的表示树$T_X$可以得到具有Hausdorff距离$d_H$的超度量空间$(\mathbf B_{X}, d_H)$的表示树通过向 $T_X$ 的每个内部顶点添加一个叶子。