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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization theorem for bounded starshaped sets in the plane


Author: Marilyn Breen
Journal: Proc. Amer. Math. Soc. 94 (1985), 693-698
MSC: Primary 52A30; Secondary 52A35
DOI: https://doi.org/10.1090/S0002-9939-1985-0792285-9
MathSciNet review: 792285
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Abstract: Let $ S$ be a nonempty bounded set in $ {R^2}$. Then $ S$ is starshaped if and only if every 3 or fewer boundary points of $ S$ are clearly visible via $ S$ from a common point of $ S$. The number 3 is best possible.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0792285-9
Keywords: Starshaped sets, convex kernel, Krasnosel'skii-type theorems
Article copyright: © Copyright 1985 American Mathematical Society