Geodesic
Description of metric space as a~classification of its finite subspaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1147-1175.

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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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     author = {Yu. A. Rylov},
     title = {Description of metric space as a~classification of its finite subspaces},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a10/}
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Yu. A. Rylov. Description of metric space as a~classification of its finite subspaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1147-1175. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a10/