Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2013, Number 6, Pages 14–19 (Mi vmumm445)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Sets with not more than two-valued metric projection on planes

A. A. Flerov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: For a set $M$ in the Euclidean plane $\mathbb{R}^2$, we prove that if any point $x\in\mathbb{R}^2$ has one or two closest points in $M$, then each point of the convex hull of $M$ lies in the segment with endpoints in $M$.
Key words: metric projection, Bunt theorem.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00952а
Received: 31.08.2012
English version:
Moscow University Mathematics Bulletin, 2013, Volume 68, Issue 6, Pages 275–280
DOI: https://doi.org/10.3103/S002713221306003X
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: A. A. Flerov, “Sets with not more than two-valued metric projection on planes”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2013, no. 6, 14–19; Moscow University Mathematics Bulletin, 68:6 (2013), 275–280
Citation in format AMSBIB
\Bibitem{Fle13}
\by A.~A.~Flerov
\paper Sets with not more than two-valued metric projection on planes
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2013
\issue 6
\pages 14--19
\mathnet{http://mi.mathnet.ru/vmumm445}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3228754}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2013
\vol 68
\issue 6
\pages 275--280
\crossref{https://doi.org/10.3103/S002713221306003X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84891697233}
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    • This publication is cited in the following 1 articles:
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