Geodesic
On Support Points and Functionals of Unbounded Convex Sets
Journal of convex analysis, Tome 20 (2013) no. 3, pp. 871-88.

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

Let K be a nonempty closed convex subset of a real Banach space of dimension at least two. Suppose that K does not contain any hyperplane. Then the set of all support points of K is pathwise connected and the set Σ1(K) of all norm-one support functionals of K is uncountable. This was proved for bounded K by L. Vesely and the author ["On support points and support functionals of convex sets", Israel J. Math. 171 (2009) 15--27], and for general K by L.Vesely ["A parametric smooth variational principle and support properties of convex sets and functions", J. Math. Anal. Appl. 350 (2009) 550--561] using a parametric smooth variational principle. We present an alternative geometric proof of the general case in the spirit of the paper of the author and L. Vesely cited above.
Classification : 46A55, 46B99, 52A07
Mots-clés : Convex set, support point, support functional, Bishop-Phelps theorem 
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     author = {C. A. De Bernardi},
     title = {On {Support} {Points} and {Functionals} of {Unbounded} {Convex} {Sets}},
     journal = {Journal of convex analysis},
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     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_3_JCA_2013_20_3_a11/}
}
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C. A. De Bernardi. On Support Points and Functionals of Unbounded Convex Sets. Journal of convex analysis, Tome 20 (2013) no. 3, pp. 871-88. http://geodesic.mathdoc.fr/item/JCA_2013_20_3_JCA_2013_20_3_a11/