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Proceedings of the American Mathematical Society

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

 

 

Generic properties of compact starshaped sets


Authors: Peter M. Gruber and Tudor I. Zamfirescu
Journal: Proc. Amer. Math. Soc. 108 (1990), 207-214
MSC: Primary 52A30; Secondary 54E52
MathSciNet review: 986649
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Abstract: A typical compact starshaped set in $ {{\text{E}}^d}$ is "small" from the topological as well as from the measure theoretic viewpoint. We formulate this more explicitly in the paper by using the notions of porosity and Hausdorff dimension. Moreover, we see that the directions of the line segments in a typical compact starshaped set are many, but not too many.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0986649-X
Article copyright: © Copyright 1990 American Mathematical Society