# Combinatorial characterization of pseudometrics

@article{Dovgoshey2020CombinatorialCO,
title={Combinatorial characterization of pseudometrics},
author={Oleksiy Dovgoshey and Juoni Luukkainen},
journal={Acta Mathematica Hungarica},
year={2020},
volume={161},
pages={257-291}
}
• Published 18 June 2019
• Mathematics
• Acta Mathematica Hungarica
Let X, Y be sets and let $$\Phi, \Psi$$ Φ , Ψ be mappings with the domains X 2 and Y 2 respectively. We say that $$\Phi$$ Φ is combinatorially similar to $$\Psi$$ Ψ if there are bijections $$f \colon \Phi(X^2) \to \Psi(Y^{2})$$ f : Φ ( X 2 ) → Ψ ( Y 2 ) and $$g \colon Y \to X$$ g : Y → X such that $$\Psi(x, y) = f(\Phi(g(x), g(y)))$$ Ψ ( x , y ) = f ( Φ ( g ( x ) , g ( y ) ) ) for all $$x, y \in Y$$ x , y ∈ Y . It is shown that the semigroups of binary relations generated by sets $$\{\Phi^{-1… 8 Citations Combinatorial properties of ultrametrics and generalized ultrametrics • O. Dovgoshey • Mathematics Bulletin of the Belgian Mathematical Society - Simon Stevin • 2020 Let X, Y be sets and let \Phi, \Psi be mappings with domains X^{2} and Y^{2} respectively. We say that \Phi and \Psi are combinatorially similar if there are bijections f \colon Ultrametric Preserving Functions and Weak Similarities of Ultrametric Spaces$$^*
• Mathematics
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