Admissible kernels for starshaped sets
Proc. Amer. Math. Soc. 82 (1981), 622-628
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Abstract: Steven Lay has posed the following interesting question: If is a convex subset of , then is there a starshaped set in whose kernel is ? Thus the problem is that of characterizing those convex sets which are admissible as the kernel of some nonconvex starshaped set in . Here Lay's problem is investigated for closed sets, and the following results are obtained: If is a nonempty closed convex subset of , then is the kernel of some planar set if and only if contains no line. If is a compact convex set in , then there is a compact set in whose kernel is .
Steven Lay, Proceedings of Conference on Convexity and Related Combinatorics, Dekker, New York, (to appear).
A. Valentine, Convex sets, McGraw-Hill Series in Higher
Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR
- Steven Lay, Proceedings of Conference on Convexity and Related Combinatorics, Dekker, New York, (to appear).
- F. A. Valentine, Convex sets, McGraw-Hill, New York, 1964. MR 0170264 (30:503)
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