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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

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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