Betweenness relation and isometric imbeddings of metric spaces - Dovgoshei, A. A.; Dordovskii, D. V. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
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 \( R \) if every three-point subspace of X is isometrically imbedded into \( R \). A series of corollaries of this theorem is obtained. We establish new criteria for finite metric spaces to be isometrically imbedded into \( R \).