Betweenness relation and isometric imbeddings of metric spaces

  • A. A. Dovgoshei
  • D. V. Dordovskii


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 \( \mathbb{R} \).
How to Cite
Dovgoshei, A. A., and D. V. Dordovskii. “Betweenness Relation and Isometric Imbeddings of Metric Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 10, Oct. 2009, pp. 1319-28,
Research articles