Geodesic
Locally Nonconical Convexity
Journal of convex analysis, Tome 8 (2001) no. 1, pp. 87-108

Voir la notice de l'article provenant de la source Heldermann Verlag

There is a hierarchy of structure conditions for convex sets. We study a recently defined condition called locally nonconical convexity (abbreviated LNC). Is is easy to show that every strictly convex set is LNC, as are half-spaces and finite intersections of sets of either of these types, but many more sets are LNC. For instance, every zonoid (the range of a nonatomic vector-valued measure) is LNC. However, there are no infinite-dimensional compact LNC sets.
Classification : 52A20, 46A55, 52A07, 46C05
Mots-clés : Convex set, locally nonconical convexity, continuous section, continuous selection, strictly convex set, zonoid 
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     author = {C. A. Akemann and G. C. Shell and N. Weaver},
     title = {Locally {Nonconical} {Convexity}},
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}
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C. A. Akemann; G. C. Shell; N. Weaver. Locally Nonconical Convexity. Journal of convex analysis, Tome 8 (2001) no. 1, pp. 87-108. http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a3/