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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of convex surfaces which are $ L$-sets


Authors: E. O. Buchman and F. A. Valentine
Journal: Proc. Amer. Math. Soc. 40 (1973), 235-239
MSC: Primary 52A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0320887-4
MathSciNet review: 0320887
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Abstract: If the surface of a bounded three dimensional convex body has the property that each pair of its points can see some third point via the surface, then with a single exception the body must be a finite cone with a convex base. The exceptional shape is that of a solid hexahedron with six triangular plane faces formed as the union of two tetrahedra having a congruent face in common.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0320887-4
Keywords: Convex surface, $ L$-set, face, exposed point, convex cone
Article copyright: © Copyright 1973 American Mathematical Society