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

 

Clear visibility and sets which are almost starshaped


Author: Marilyn Breen
Journal: Proc. Amer. Math. Soc. 91 (1984), 607-610
MSC: Primary 52A30
MathSciNet review: 746099
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Abstract: Let $ S$ be a nonempty compact connected set in $ {R^2}$. Assume that every two points of local nonconvexity of $ S$ are clearly visible from a common point of $ S$. Then $ S$ is "almost" starshaped. In fact, for any point $ y$ in $ {R^2}$ there is a line $ L$ through $ y$ such that $ L \cap S$ is convex and every point of $ S$ sees via $ S$ a point of $ L$. If "clearly visible" is replaced by the weaker term "visible", then the result fails.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746099-5
PII: S 0002-9939(1984)0746099-5
Article copyright: © Copyright 1984 American Mathematical Society