This article is cited in 7 papers

Successive in rank $(n+1,2)$ embedding of dimetric phenomenologically symmetric geometries of two sets

R. A. Bogdanova, G. G. Mikhailichenko, R. M. Muradov

Gorno-Altaisk State University, 1 Lenkina str., Gorno-Altaisk, 649000, Russia

Abstract: Is known complete classification of dimetric phenomenologically symmetrical geometries of two sets of rank $(n+1, 2)$, where $n=1,2, \ldots{}$ . From that classification it can be seen that some geometries of higher rank include in it geometries of previous rank. Such embedding can be proved (or disproved) by solving corresponding functional equation in which fact of embedding of geometries is expressed on language of metric functions that define them.

Keywords: geometry of two sets, metric function, phenomenological symmetry, embedding of geometries, functional equation.

UDC: 514.1:517.965

Received: 29.05.2019
Revised: 29.05.2019
Accepted: 25.09.2019

DOI: 10.26907/0021-3446-2020-6-9-14

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:6, 6–10

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