Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces

被引：0
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作者：
Oleksiy Dovgoshey
Mehmet Küçükaslan
机构：
[1] Institute of Applied Mathematics and Mechanics of NASU,Department of Theory of Functions
[2] Institut fuer Mathematik Universitaet zu Luebeck,Department of Mathematics, Faculty of Science and Arts
[3] Mersin University,undefined
来源：
Annals of Combinatorics | 2022年 / 26卷
关键词：
Locally finite tree; Rayless tree; Compactness; Completeness; Total boundedness; Primary 05C63; 05C05; Secondary 54E35;
D O I：
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学科分类号：
摘要：
We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.
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页码：613 / 642
页数：29
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