On Euclidean images of a set endowed with a preordonnance (Q1821721)

The purpose of the paper is to study Euclidean representations of (I,R), where I is a finite nonempty set, and R is a total order of \(I^ 2\) satisfying for arbitrary \((i,j,k)\in I^ 3\) (i,i)R(j,k), and (j,i)R(i,j) (R is called a preordonnance on I). New results concerning the determination of ultrametric preordonnances, upper bounds for certain determinations, and dimensions of the spaces where a given preordonnance may have an image are established.