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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 6, Pages 1231–1244 (Mi smj2378)  
This article is cited in 1 scientific paper (total in 1 paper)

Quasispaces induced by vector fields measurable in $\mathbb R^3$

A. V. Belykh, A. V. Greshnov

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (336 kB) Citations (1)
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Abstract: We study some metric functions that are induced by a class of basis vector fields in $\mathbb R^3$ with measurable coordinates. These functions are proved to be quasimetrics in the domain of definition of the vector fields. Under some natural constraints, the Rashevsky–Chow Theorem and the Ball-Box Theorem are established for the classes of vector fields we consider.
Keywords: vector field, quasimetric, generalized triangle inequality, horizontal curve.
Received: 03.06.2010
Revised: 19.07.2012
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 6, Pages 984–995
DOI: https://doi.org/10.1134/S0037446612060031
Bibliographic databases:
Document Type: Article
UDC: 514.763+512.812.4+517.911
Language: Russian
Citation: A. V. Belykh, A. V. Greshnov, “Quasispaces induced by vector fields measurable in $\mathbb R^3$”, Sibirsk. Mat. Zh., 53:6 (2012), 1231–1244; Siberian Math. J., 53:6 (2012), 984–995
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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