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 
@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},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a15/}
}
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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/