This article is cited 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

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.

UDC: 517.982.256

Received: 31.08.2012

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2013, 68:6, 275–280

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