Abstract
A lattice cone of functions on a set X is a convex cone of bounded real-valued functions on X which contains the constants and which is closed under the lattice operations. Our principal results concern the relation between closed lattice cones on a set X and certain binary relations, called inclusions, on the power set of X. These results are applied to interposition problems, Császár compactifications of quasi-proximity spaces, the compactification of Nachbin’s completely regular ordered topological spaces, and a problem in best approximation.
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