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Ultrametric Preserving Functions and Weak Similarities of Ultrametric Spaces\(^*\)

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Abstract

Let \(WS(X, d)\) be the class of ultrametric spaces which are weakly similar to ultrametric space \((X, d)\). The main results of the paper completely describe the ultrametric spaces \((X, d)\) for which the equality

$$\rho(x, y) = f(d(\Phi(x), \Phi(y)))$$

holds for every \((Y, \rho) \in WS(X, d)\), every weak similarity \(\Phi \colon Y \to X\), and all \(x\), \(y \in Y\) with some ultrametric (pseudoultrametric) preserving function \(f\) depending on \(\Phi\).

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Funding

Viktoriia Bilet and Oleksiy Dovgoshey were partially supported in the frame of project 0117U002165: Development of Mathematical Models, Numerical and Analytical Methods, and Algorithms for Solving Modern Problems of Biomedical Research.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of NASU, Dobrovolskogo str. 1, 84100, Slovyansk, Ukraine

    Viktoriia Bilet & Oleksiy Dovgoshey

  2. Odesa I. I. Mechnikov National University, Dvoryanskaya str. 2, 65082, Odesa, Ukraine

    Ruslan Shanin

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  1. Viktoriia Bilet
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  2. Oleksiy Dovgoshey
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  3. Ruslan Shanin
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Correspondence to Viktoriia Bilet, Oleksiy Dovgoshey or Ruslan Shanin.

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Bilet, V., Dovgoshey, O. & Shanin, R. Ultrametric Preserving Functions and Weak Similarities of Ultrametric Spaces\(^*\). P-Adic Num Ultrametr Anal Appl 13, 186–203 (2021). https://doi.org/10.1134/S207004662103002X

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