Clear visibility and sets which are almost starshaped
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- by Marilyn Breen PDF
- Proc. Amer. Math. Soc. 91 (1984), 607-610 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 607-610
- MSC: Primary 52A30
- DOI: https://doi.org/10.1090/S0002-9939-1984-0746099-5
- MathSciNet review: 746099