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The Embedding of Compact Convex Sets in Locally Convex Spaces

Published online by Cambridge University Press:  20 November 2018

James W. Roberts
James W. Roberts*
Affiliation:
University of South Carolina, Columbia, South Carolina
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In studying compact convex sets it is usually assumed that the compact convex set X is contained in a Hausdorff topological vector space L where the topology on X is the relative topology. Usually one assumes that L is locally convex. The reason for this is that most of the major theorems such as the Krein-Milman, Choquet-Bishop-de Leeuw, and most of the fixed point theorems require that there be enough continuous affine functions on X to separate points.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978 , pp. 449 - 454
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Choquet, G., Lectures on analysis, Vol. I (W. A. Benjamin, New York, 1969).Google Scholar
2. Hewitt, E. and Stromberg, K., Real and abstract analysis (Springer-Verlag, New York, 11)05).Google Scholar
3. Jamison, R. E., O'Brien, R. C. and Taylor, P. D., On embedding a compact convex set into a locally convex topological vector space, Pac. J. Math. 64 (1976), 193–205).Google Scholar
4. Roberts, J. W., A generalization of compact convex sets, to appear.Google Scholar
5. Roberts, J. W., Representing measures in compact groupoids, 111. J. Math. 19 (1975), 277–291.Google Scholar
6. Phelps, R. R., Lectures on Choquet's theorem (Van Nostrand, 1966).Google Scholar