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arXiv · 2412.20539

Weak similarities of finite ultrametric and semimetric spaces

Evgeniy Petrov
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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 $\Phi\colon X\to Y$. 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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Evgeniy Petrov. 2024-12-29. Weak similarities of finite ultrametric and semimetric spaces. https://doi.org/10.1134/s2070046618020048

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