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The Continuity of the Visibility Function on a Starshaped Set

Published online by Cambridge University Press:  20 November 2018

Gerald Beer
Gerald Beer*
Affiliation:
University of California, Los Angeles, California
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The visibility function assigns to each point x of a fixed measurable set E in a Euclidean space En the Lebesgue outer measure of S(x), the set {y : rx + (1 — r)y ∊ E for every r in [0, 1]}.

The purpose of this paper is to determine sufficient conditions for the continuity of the function on the interor of a starshaped set.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 989 - 992
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Gerald, Beer, The index of convexity and the visibility function (to appear in Pacific J. Math.).Google Scholar
2. Gerald, Beer, Continuity properties of the visibility function (to appear).Google Scholar
3. Valentine, F. A., Convex sets (McGraw-Hill, New York, 1964).Google Scholar