Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T05:33:25.015Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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