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Proceedings of the American Mathematical Society

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

 

 

Too long shadow boundaries


Author: Tudor Zamfirescu
Journal: Proc. Amer. Math. Soc. 103 (1988), 587-590
MSC: Primary 52A20; Secondary 54E52
DOI: https://doi.org/10.1090/S0002-9939-1988-0943088-6
MathSciNet review: 943088
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Abstract: It is shown that, in the sense of Baire categories, most $ d$-dimensional convex bodies have infinitely long shadow boundaries if the light comes along one of many $ \left( {d - 2} \right)$-dimensional subspaces. This reveals (once again!) a striking contrast between the categorical and the measure-theoretical points of view.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943088-6
Article copyright: © Copyright 1988 American Mathematical Society