TY - JOUR
AU - A. A. Dovgoshei
AU - D. V. Dordovskii
PY - 2009/10/25
Y2 - 2023/03/29
TI - Betweenness relation and isometric imbeddings of metric spaces
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 61
IS - 10
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3103
AB - 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 \( \mathbb{R} \).
ER -