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On a Problem of Klee

Published online by Cambridge University Press:  20 November 2018

N. M. Stavrakas  and
R. E. Jamison
N. M. Stavrakas
Affiliation:
Clemson University, Clemson, South Carolina
R. E. Jamison
Affiliation:
Clemson University, Clemson, South Carolina
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Let E be a Hausdorff topological vector space. A subset A of E is a polytope iff A is the convex hull of a finite number of points. In this note a necessary condition for every maximal convex subset of a subset B of E to be a polytope is given. This is related to a problem first posed by Klee [1] for compact three-cells in Euclidean 3 space.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 125 - 126
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Klee, V. L., Some characterizations of convex polyhedra, Acta Math. 102 (1959), 79-107.Google Scholar
2. Valentine, F. A., Convex sets, McGraw-Hill, New York (1964), 6-7.Google Scholar