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Weak Similarities of Finite Ultrametric and Semimetric Spaces

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Abstract

Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces X and Y are weakly similar if there exists a weak similarity Φ: X → Y. We find a structural characteristic of finite ultrametric spaces for which the isomorphism of its representing trees implies a weak similarity of the spaces. We also find conditions under which the Hasse diagrams of balleans of finite semimetric spaces are isomorphic.

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Authors and Affiliations

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

    Evgeniy Petrov

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  1. Evgeniy Petrov
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Correspondence to Evgeniy Petrov.

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The text was submitted by the authors in English.

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Petrov, E. Weak Similarities of Finite Ultrametric and Semimetric Spaces. P-Adic Num Ultrametr Anal Appl 10, 108–117 (2018). https://doi.org/10.1134/S2070046618020048

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  • DOI: https://doi.org/10.1134/S2070046618020048

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