# 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} }

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

- MathematicsBulletin of the Belgian Mathematical Society - Simon Stevin
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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…

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. It is well-known that a metric space ( X, d ) is complete iﬀ the set X is closed in every metric superspace of ( X, d ) . For a given pseudometric space ( Y, ρ ) , we describe the maximal class CEC…

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Let (X, d) be an unbounded metric space. To investigate the asymptotic behavior of (X, d) at infinity, one can consider a sequence of rescaling metric spaces (X, 1 rn d) generated by given sequence…

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For arbitrary semimetric space ( X, d ) and disjoint proximinal subsets A , B of X we deﬁne the proximinal graph as a bipartite graph with parts A and B whose edges { a, b } satisfy the equality d (…

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