Finite Ultrametric Balls
The necessary and sufficient conditions under which a given family ℱ of subsets of finite set X coincides with the family 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 ( B X , d H ) with the Hausdorff distance d H can...
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| Veröffentlicht in: | P-adic numbers, ultrametric analysis, and applications ultrametric analysis, and applications, 2019-07, Vol.11 (3), p.177-191 |
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| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The necessary and sufficient conditions under which a given family ℱ of subsets of finite set
X
coincides with the family
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 (
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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| ISSN: | 2070-0466 2070-0474 |
| DOI: | 10.1134/S2070046619030014 |