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Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces

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Abstract

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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Acknowledgements

The authors wish to express their gratitude to the referee for a number of valuable corrections.

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Authors and Affiliations

  1. Department of Theory of Functions, Institute of Applied Mathematics and Mechanics of NASU, Dobrovolskogo Str. 1, Slovyansk, 84100, Ukraine

    Oleksiy Dovgoshey

  2. Institut fuer Mathematik Universitaet zu Luebeck, Ratzeburger Allee 160, 23562, Luebeck, Deutschland

    Oleksiy Dovgoshey

  3. Department of Mathematics, Faculty of Science and Arts, Mersin University, 33343, Mersin, Turkey

    Mehmet Küçükaslan

Authors
  1. Oleksiy Dovgoshey
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  2. Mehmet Küçükaslan
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Correspondence to Oleksiy Dovgoshey.

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Communicated by Victor Chepoi.

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Dovgoshey, O., Küçükaslan, M. Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces. Ann. Comb. 26, 613–642 (2022). https://doi.org/10.1007/s00026-022-00581-8

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  • DOI: https://doi.org/10.1007/s00026-022-00581-8

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