Geodesic
A Characterization of Starshaped Sets
Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 673-680

Voir la notice de l'article provenant de la source Cambridge University Press

In 1946 Krasnoselskii proved that if every n + 1 points of a compact connected set S in a Euclidean space En can see at least one point of S via S then S is starshaped [1]. This result was expanded by Robkin in 1965 [2]. In this paper, we characterize starshaped sets in En by a local arcwise convexity property relative to a point p. 
Stanek, Jean Chan. A Characterization of Starshaped Sets. Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 673-680. doi: 10.4153/CJM-1977-070-2
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[1] 1. Krasnoselskii, M. A., Sur un critère pour qu'un domain soit étoile, Mat. Sb., N.S. 19, no. 61, (1946), 309–310. Google Scholar

[2] 2. Robkin, E. E., Characterizations of starshaped sets, Doctoral Dissertation, University of California, Los Angeles, 1965. Google Scholar

[3] 3. Valentine, F. A., Arcwise convex sets, Proc. Am. Math. Soc. 2 (1951), 159–165. Google Scholar

[4] 4. Tietze, H., Uber Konvexheit im kleinen und im grossen und ùber gewisse den Punkten einer Menge zugeordnete Dimensionszahlen, Math. Z. 28 (1928), 697–707. Google Scholar

[5] 5. Valentine, F. A., Convex sets (McGraw-Hill Book Company, New York, 1964). Google Scholar

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