2022/11/07 by A. Kh. Galstyan, Galstyan, A. Kh. · 1 citation
Computer Science · Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Engineering Technology and Methodologies #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2211.03847
openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.