Том 71
№ 4

All Issues

Dordovskii D. V.

Articles: 1
Article (Russian)

Betweenness relation and isometric imbeddings of metric spaces

Dordovskii D. V., Dovgoshei A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1319-1328

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 \( \mathbb{R} \).