Betweenness relation and isometric imbeddings of metric spaces

• Date: 2009
• Main Authors: Dovgoshei, A. A., Dordovskii, D. V., Довгошей, А. А., Дордовский, Д. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3103
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...