Classification of Finite Subspaces of Metric Space Instead of Constraints on Metrics

Abstract

A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only metric. It admits to remove constraints imposed usually on metric (the triangle axiom and nonnegativity of the squared metric), and to use the metric space for description of the space-time and other geometries with indefinite metric. Describing space-time and using this method, one can explain quantum effects as geometric effects, i.e. as space-time properties