Abstract
A closed convex subsetQ of a compact convex setK is said to have the extension property if every continuous affine function onQ can be extended to a continuous affine function onK. It is proved that the extension property is equivalent to the existence of a numberN such that is any direction in whichQ has positive width, the ratio of the width ofK to the width ofQ is less thanN.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. M. Alfsen,Facial structure of compact convex sets, Proc. London Math. Soc.18, Series 3, (1968).
E. M. Alfsen,Convex Sets and Boundary Integrals Springer, Ergebnisse Tracts No. 57, Springer-Verlag, Heidelberg, 1971.
J. L. Kelly, and I. Namioka,Linear Topological Spaces, Van Nostrand, Princeton, N.J., 1963.
L. H. Loomis,An Introduction to Abstract Harmonic Analysis, Van Nostrand, Princeton, N.J., 1953.
L. Asimow,Directed Banach spaces of affine functions, Trans. Amer. Math. Soc.,143 (1969), 117–132.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Taylor, P.D. The extension property for compact convex sets. Israel J. Math. 11, 159–163 (1972). https://doi.org/10.1007/BF02762617
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02762617