@article{Dovgoshei_Dordovskii_2009, title={Betweenness relation and isometric imbeddings of metric spaces}, volume={61}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3103}, abstractNote={We give an elementary proof of the classical Menger result according to which any metric space <em class="EmphasisTypeItalic ">X</em> that consists of more than four points is isometrically imbedded into <span class="InlineEquation" id="IEq1">\( \mathbb{R} \)</span> if every three-point subspace of <em class="EmphasisTypeItalic ">X</em> is isometrically imbedded into <span class="InlineEquation" id="IEq2">\( \mathbb{R} \)</span>. A series of corollaries of this theorem is obtained. We establish new criteria for finite metric spaces to be isometrically imbedded into <span class="InlineEquation" id="IEq3">\( \mathbb{R} \)</span>.}, number={10}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Dovgoshei, A. A. and Dordovskii, D. V.}, year={2009}, month={Oct.}, pages={1319-1328} }