### Metric Space: Classification of Finite Subspaces instead
of Constraints on Metric

Yuri A.Rylov

Institute for Problems in Mechanics, Russian Academy of
Sciences,
101, bld.1 Vernadskii Ave. , Moscow, 117526, Russia.
e-mail: rylov@ipmnet.ru
#### Abstract

A new method of metric space investigation, based on classification
of its finite subspaces, is suggested. It admits one to derive information
on metric space properties which is encoded in metric and to describe geometry
in terms of only metric. The method admits one to remove constraints imposed
usually on metric (the triangle axiom and nonnegativity of the squared
metric). Elimination of the triangle axion leads to "tubular generalization"
of metric geometry (T-geometry), when the shortests are replaced by hallow
tubes. Elimination of the second constraint admits one to use the metric
space for description of the space-time and other geometries with indefinite
metric.

Text of the paper in Postscript format
in English, Figure in Postscript format

Text of the paper in Postscript format
in Russian, Figure in Postscript format

Updated 10/10/99