About the continuity of one operation with convex compacts in finite–dimensional normed spaces
https://doi.org/10.22405/2226-8383-2022-23-5-152-160
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.
About the Author
Arsen Khachaturovich Galtyan
Lomonosov Moscow State University
Russian Federation
Russian Federation
postgraduate student
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Review
For citations:
Galtyan A.Kh. About the continuity of one operation with convex compacts in finite–dimensional normed spaces. Chebyshevskii Sbornik. 2022;23(5):152-160. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-5-152-160
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