Decomposition of finite pseudometric spaces (Q1272279)

From the summary (translation): For pseudometrics the property of decomposability (indecomposability) is defined, which is the possibility (impossibility) to represent the pseudo-metric as a sum of two pseudometrics by any other method except the partition of all distances in equal proportion. It is proved that for a given finite number \(n\) of points there exists a collection of a finite number of indecomposable pseudometrics (base), which generates by means of linear combination with nonnegative coefficients the set of all pseudometrics. All base components for \(n\leq 7\) are enumerated. A procedure for determining decomposability or indecomposability of an arbitrary finite pseudometric space is introduced. Some indications for decomposability and indecomposability are established.