α-集与弱凸Vial集的关系

VIII Information school of a young scientist Central Scientific Library of the Urals Branch of the Russian Academy of Science Pub Date : 2020-12-16 DOI:10.32460/ISHMU-2020-8-0017

D. B. Davletov, A. Ershov, A. Ershova

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摘要

本文研究了α-集的性质，α-集是凸集的推广。建立了α-集与弱凸集之间的关系。证明了具有有界Chebyshev半径的弱凸val集是α- 1。文中给出了一个例子，证明反之不成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Relationship between α-sets and weakly convex Vial sets

In the paper, we study properties of the α-sets, which are generalizations of the convex sets. Relationship between the α-sets and weakly convex sets is established. It is proved that the weakly convex Vial sets with bounded Chebyshev radius are α-ones. An example is given showing that the converse is not true.

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VIII Information school of a young scientist Central Scientific Library of the Urals Branch of the Russian Academy of Science

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