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Support properties of a family of connected compact sets. (English) Zbl 0982.15003

Summary: A problem of finding a system of proportionally located parallel supporting hyperplanes of a family of connected compact sets is analyzed. Special attention is paid to finding a common supporting halfspace. An existence theorem is proved and a method of solution is proposed.

MSC:

15A03 Vector spaces, linear dependence, rank, lineability
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
52B55 Computational aspects related to convexity
90C34 Semi-infinite programming
15A39 Linear inequalities of matrices
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