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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

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