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This article is cited in 1 scientific paper (total in 1 paper)
BRIEF MESSAGES
About the continuity of one operation with convex compacts in finite–dimensional normed spaces
A. Kh. Galstyan Lomonosov Moscow State University (Moscow)
Abstract:
In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite–dimensional normed spaces, in the case when both compact sets are non-empty convex subsets, such an operation is continuous in the topology generated by the Hausdorff metric.
The question of the continuous dependence of the described intersection on the radius of the neighborhood arose as a by–product of the development of the theory of extremal networks. However, it turned out to be interesting in itself, suggesting various generalizations. Therefore, it was decided to publish it separately.
Keywords:
metric geometry, convex sets, Hausdorff distance, continuous deformations.
Received: 15.06.2022 Accepted: 22.12.2022
Citation:
A. Kh. Galstyan, “About the continuity of one operation with convex compacts in finite–dimensional normed spaces”, Chebyshevskii Sb., 23:5 (2022), 152–160
Linking options:
https://www.mathnet.ru/eng/cheb1262 https://www.mathnet.ru/eng/cheb/v23/i5/p152
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Abstract page: | 68 | Full-text PDF : | 19 | References: | 10 |
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