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Finite Ultrametric Balls

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 نشر من قبل Oleksiy Dovgoshey
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف O. Dovgoshey




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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 $T_X$.



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