Journal of Convex Analysis 18 (2011), No. 3, 855--864
Copyright Heldermann Verlag 2011
Continuous Selections, Free Vector Lattices and Formal Minkowski Differences
Reinhard Börger
Fakultät für Mathematik und Informatik, Fernuniversität, 58084 Hagen, Germany
Reinhard.Boerger@FernUni-Hagen.de
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.
Keywords: Vector lattice, polyhedral functional, polytope, support functional, Minkowski sum.
MSC: 46A40, 52A25, 06D99, 08B11
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