FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1147-1175

Yu. A. Rylov

Abstract

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```
We suggest a new method of metric space description, using
its constituents (finite metric subspaces) as basic objects of
description. The method allows one to obtain information about
the metric space properties from the metric and to describe
the metric space geometry in terms of its constituents
and metric only.
The suggested method permits one to remove the constraints
imposed usually on metric (the triangle axiom and non-negativity
of the squared metric).
Elimination of these constraints leads to a new non-degenerate
geometry. This geometry is called tubular geometry
(T-geometry),
because in this geometry the shortest paths are replaced by hollow
tubes. The T-geometry may be used for description of
the space-time and of other geometries with indefinite metric.
```

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Last modified: April 17, 2002