A characterization theorem for bounded starshaped sets in the plane

Breen, Marilyn

doi:10.1090/S0002-9939-1985-0792285-9

A characterization theorem for bounded starshaped sets in the plane
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Proc. Amer. Math. Soc. 94 (1985), 693-698 Request permission

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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