Continuous Selections, Free Vector Lattices and Formal Minkowski Differences

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.