Geodesic
The Embedding of Compact Convex Sets in Locally Convex Spaces
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 449-454

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Roberts, James W. The Embedding of Compact Convex Sets in Locally Convex Spaces. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 449-454. doi: 10.4153/CJM-1978-038-0
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