Abstract
It is shown that if a closed setS in the plane is (n+1)-convex, then it has no more thann 4 holes. As a consequence, it can be covered by≤n 6 convex subsets. This is an improvement on the known bound of 2n·n 3.
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The author would like to thank the BSF for partially supporting this research. Publication no. 354.
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Perles, M.A., Shelah, S. A closed (n + 1)-convex set inR 2 is a union ofn 6 convex sets. Israel J. Math. 70, 305–312 (1990). https://doi.org/10.1007/BF02801466
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DOI: https://doi.org/10.1007/BF02801466