2017
Том 69
№ 9

All Issues

Betweenness relation and isometric imbeddings of metric spaces

Dordovskii D. V., Dovgoshei A. A.

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Abstract

We give an elementary proof of the classical Menger result according to which any metric space X that consists of more than four points is isometrically imbedded into \( \mathbb{R} \) if every three-point subspace of X is isometrically imbedded into \( \mathbb{R} \). A series of corollaries of this theorem is obtained. We establish new criteria for finite metric spaces to be isometrically imbedded into \( \mathbb{R} \).

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 10, pp 1556-1567.

Citation Example: Dordovskii D. V., Dovgoshei A. A. Betweenness relation and isometric imbeddings of metric spaces // Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1319-1328.

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