Betweenness relation and isometric imbeddings of metric spaces

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

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 \( \mathbb{R} \).
Published
25.10.2009
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, https://umj.imath.kiev.ua/index.php/umj/article/view/3103.
Section
Research articles