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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Starshaped unions and nonempty intersections of convex sets in $ {\bf R}\sp d$


Author: Marilyn Breen
Journal: Proc. Amer. Math. Soc. 108 (1990), 817-820
MSC: Primary 52A35; Secondary 52A30
MathSciNet review: 990413
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Abstract: Let $ \mathcal{G}$ be a nonempty family of compact convex sets in $ {R^d},d \geq 1$. Then every subfamily of $ \mathcal{G}$ consisting of $ d + 1$ or fewer sets has a starshaped union if and only if $ \cap \{ G:G{\text{ in }}\mathcal{G}\} \ne \emptyset $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0990413-5
PII: S 0002-9939(1990)0990413-5
Article copyright: © Copyright 1990 American Mathematical Society