A characterization theorem for bounded starshaped sets in the plane-Reference-Cited by-同舟云学术

A characterization theorem for bounded starshaped sets in the plane

Published:1985 Issue:4 Volume:94 Page:693-698
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Breen Marilyn

Abstract

Let S S be a nonempty bounded set in R 2 {R^2} . Then S S is starshaped if and only if every 3 or fewer boundary points of S S are clearly visible via S S from a common point of S S . The number 3 is best possible.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1985-094-04/S0002-9939-1985-0792285-9/S0002-9939-1985-0792285-9.pdf

Reference8 articles.

1. A Krasnosel′skiĭ-type theorem for points of local nonconvexity;Breen, Marilyn;Proc. Amer. Math. Soc.,1982

2. Points of local nonconvexity and sets which are almost starshaped;Breen, Marilyn;Geom. Dedicata,1982

3. The dimension of the kernel of a planar set;Breen, Marilyn;Pacific J. Math.,1979

4. The dimension of the convex kernel of a compact starshaped set;Falconer, K. J.;Bull. London Math. Soc.,1977

5. Intersections of maximal starshaped sets;Hare, W. R., Jr.;Proc. Amer. Math. Soc.,1968

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