GENERALIZED METRICS – \((n,m,\rho)\)-METRICS

Abstract

In this paper we introduce the notion of generalized, i.e. \((n,m,\rho)\)-metrics, which is a generalization of the usual notion for metrics, and which coincide with it for \(n=2\), \(m=1\) and \(\rho\) the identity relation. In the case \(m=1\), we use the notation \((n,\rho)\)-metric. With this notions, the area of triangles in the plane is a \((3,\rho)\)-metric, and the volume of tetrahedra in the space is a \((4,\rho)\)-metric.