This article is cited in 7 papers

Ptolemaic spaces

A. A. Dovgosheĭ, E. A. Petrov

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk, Ukraine

Abstract: We show that equilateral pseudolinear quadruples are in a certain sense extremally non-Ptolemaic metric spaces. We find four-point pseudometric spaces that are maximally Ptolemaic.

Keywords: Ptolemaic space, extremal problem on a finite metric space, pseudometric space, pseudolinear quadruple, isoperimetric inequality.

UDC: 514.177+515.124.4

Received: 30.08.2010

 English version: Siberian Mathematical Journal, 2011, 52:2, 222–229

Bibliographic databases:

• 
• 
•