Geodesic
Continuous Selections, Free Vector Lattices and Formal Minkowski Differences
Journal of convex analysis, Tome 18 (2011) no. 3, pp. 855-864

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

We investigate the vector lattice of continuous selections of linear functionals on a topological vector space. In particular, we show that it is a free vector lattice on n generators and can be constructed as vector lattice of formal Minkowski differences of polytopes. This can be used to show that every (set-theoretically) minimal representation of polytopes is a representation of a (formal) difference of polytopes.
Classification : 46A40, 52A25, 06D99, 08B11
Mots-clés : Vector lattice, polyhedral functional, polytope, support functional, Minkowski sum 
R. Börger. Continuous Selections, Free Vector Lattices and Formal Minkowski Differences. Journal of convex analysis, Tome 18 (2011) no. 3, pp. 855-864. http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a15/
@article{JCA_2011_18_3_JCA_2011_18_3_a15,
     author = {R. B\"orger},
     title = {Continuous {Selections,} {Free} {Vector} {Lattices} and {Formal} {Minkowski} {Differences}},
     journal = {Journal of convex analysis},
     pages = {855--864},
     year = {2011},
     volume = {18},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a15/}
}
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