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An Example Concerning Exposed Points

Published online by Cambridge University Press:  20 November 2018

M. Edelstein
M. Edelstein*
Affiliation:
Michigan State University, E. LansingMichiganU.S.A.and Dalhousie University, HalifaxN. S.Canada
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In his paper [1] V. L. Klee gave an example of a smooth bounded convex body C, in En, with the property that extC s closed and extC - expC is dense in extC. As in [1] extC and expC denote the sets of extreme and exposed points of C respectively. It is the purpose of this note to exhibit a similar example in a general separable Banach space using a direct construction which involves Minkowski summation of convex sets.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 3 , April 1965 , pp. 323 - 327
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Klee, V. L., Extremal structure of convex sets II, Math. Zeitscrift 69 (1958), 90-114.CrossRefGoogle Scholar
2. Day, M. M., Strict convexity and smoothness of normed spaces, Trans. Am, Math. Soc. 78 (1955), 516-528.CrossRefGoogle Scholar