The Pythagorean-Riemannian space corresponds to only one such equivalence class, defined by F²_p = (dx¹)² + ⋯ + (dxⁿ)²

To every possible equivalence class [\(F\)] of homogeneous functions, there corresponds a type of metrical space. The Pythagorean-Riemannian space, for which \(F^{2}_{p} = (dx^{1})^{2} + \cdots + (dx^{n})^{2}\), is one among several types of possible metrical spaces. The problem, therefore, is to single out the equivalence class \([F]\), where \(F\) corresponds to \(F^{2}_{p} = (dx^{1})^{2} + \cdots + (dx^{n})^{2}\), from the other possibilities, and to provide arguments for this preferen